Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, ...Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, we consider constructing binary linear codes by combining deep holes with binary BCH codes. In this article, we consider the 2-error-correcting binary primitive BCH codes and the extended codes to construct new binary linear codes by combining them with deep holes, respectively. Furthermore, three classes of binary linear codes are constructed, and then we determine the parameters and the weight distributions of these new binary linear codes.展开更多
Abraham Lempel et al made a connection between linear codes and systems of bilinear forms over finite fields. In this correspondence, a new simple proof of a theorem in [1] is presented; in addition, the encoding proc...Abraham Lempel et al made a connection between linear codes and systems of bilinear forms over finite fields. In this correspondence, a new simple proof of a theorem in [1] is presented; in addition, the encoding process and the decoding procedure of RS codes are simplified via circulant matrices. Finally, the results show that the correspondence between bilinear forms and linear codes is not unique.展开更多
m-weight, as a new generalization of classical Hamming weight, was discussedin this paper. A condition for the existence of linear codes of certain m-weights was given; theSingleton bound, Plotkin bound and Sphere Par...m-weight, as a new generalization of classical Hamming weight, was discussedin this paper. A condition for the existence of linear codes of certain m-weights was given; theSingleton bound, Plotkin bound and Sphere Parking bound of Hamming weight were correspondinglygeneralized to the m-weight.展开更多
Secret sharing is an important topic in cryptography and has applications in information security. The coding theory has been an important role in the constructing of secret sharing schemes. It is known that every lin...Secret sharing is an important topic in cryptography and has applications in information security. The coding theory has been an important role in the constructing of secret sharing schemes. It is known that every linear code can be used to construct secret sharing schemes. So, we use the parity-check matrix of a linear code to construct secret sharing schemes based on linear codes. We also describe some techniques to recover the secret and determine the access structure of the new scheme. In this paper, we use the Massey＇s secret sharing scheme.展开更多
In this paper,we first give the definition of the Euclidean sums of linear codes,and prove that the Euclidean sums of linear codes are Euclidean dual-containing.Then we construct two new classes of optimal asymmetric ...In this paper,we first give the definition of the Euclidean sums of linear codes,and prove that the Euclidean sums of linear codes are Euclidean dual-containing.Then we construct two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of the Reed-Solomon codes,and two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of linear codes generated by Vandermonde matrices over finite fields.Moreover,these optimal asymmetric quantum errorcorrecting codes constructed in this paper are different from the ones in the literature.展开更多
Recently,linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes,constant composition codes,strongly regular graphs and so on.In this paper,based on the Weil s...Recently,linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes,constant composition codes,strongly regular graphs and so on.In this paper,based on the Weil sums,several classes of two-weight or three-weight linear codes are presented by choosing a proper defining set,and their weight enumerators and complete weight enumerators are determined.Furthermore,these codes are proven to be minimal.By puncturing these linear codes,two classes of two-weight projective codes are obtained,and the parameters of the corresponding strongly regular graph are given.This paper generalizes the results of[7].展开更多
In this paper, the MacWilliams type identity for the m-ply Lee weight enumerator for linear codes over F2 ＋uF2 is determined. As an application of this identity, the authors obtain a MacWilliams type identity on Lee ...In this paper, the MacWilliams type identity for the m-ply Lee weight enumerator for linear codes over F2 ＋uF2 is determined. As an application of this identity, the authors obtain a MacWilliams type identity on Lee weight for linear codes over F2m ＋ uF2m. Furthermore, the authors prove a duality for the m-ply Lee weight distributions by taking advantage of the Krawtchouk polynomials.展开更多
The Lee weight enumerators and the complete weight enumerators for the linear codes over ring R = F2 ＋ u F2 ＋ v F2 are defined and Gray map from R^nto F2^3n is constructed. By proving the fact that the Gray images o...The Lee weight enumerators and the complete weight enumerators for the linear codes over ring R = F2 ＋ u F2 ＋ v F2 are defined and Gray map from R^nto F2^3n is constructed. By proving the fact that the Gray images of the self-dual codes over R are the self-dual codes over F2, and based on the Mac Williams identities for the Hamming weight enumerators of linear codes over F2, the Mac Williams identities for Lee weight enumerators of linear codes over R are given. Further, by introducing a special variable t, the Mac Williams identities for the complete weight enumerators of linear codes over R are obtained. Finally, an example which illustrates the correctness and function of the two Mac Williams identities is provided.展开更多
Highly nonlinear resilient functions play a crucial role in nonlinear combiners which are usual hardware oriented stream ciphers.During the past three decades,the main idea of construction of highly nonlinear resilien...Highly nonlinear resilient functions play a crucial role in nonlinear combiners which are usual hardware oriented stream ciphers.During the past three decades,the main idea of construction of highly nonlinear resilient functions are benefited from concatenating a large number of affine subfunctions.However,these resilient functions as core component of ciphers usually suffered from the guess and determine attack or algebraic attack since the n-variable nonlinear Boolean functions can be easily given rise to partial linear relations by fixing at most nil variables of them.How to design highly nonlinear resilient functions(S-boxes)without concatenating a large number of nil variables affine subfunctions appears to be an important task.In this article,a new construction of highly nonlinear resilient functions is proposed.These functions consist of two classes subfunctions.More specially,the first class(nonlinear part)contains both the bent functions with 2k variables and some affine subfUnctions with n/2-k variables which are attained by using[n/2-k,m,d]disjoint linear codes.The second class(linear part)includes some linear subfunctions with nil variables which are attained by using[n/2,m,d]disjoint linear codes.It is illustrated that these resilient functions have high nonlinearity and high algebraic degree.In particular,It is different from previous well-known resilient S-boxes,these new S-boxes cannot be directly decomposed into some affine subftinctions with nil variables by fixing at most nil variables.It means that the S-boxes(vectorial Boolean functions)which use these resilient functions as component functions have more favourable cryptography properties against the guess and determine attack or algebraic attacks.展开更多
Linear dispersion codes (LDCs) were originally designed based on maximum likelihood detection. They do not have good performance when using ordered successive interference cancellation (OSIC) detection. In this paper,...Linear dispersion codes (LDCs) were originally designed based on maximum likelihood detection. They do not have good performance when using ordered successive interference cancellation (OSIC) detection. In this paper,we propose a new improved linear dispersion codes transmission scheme to combat performance loss of original LDCs when using OSIC detection. We introduce an interleaver to each data substream transmitted over different antennas after LDCs encoder. Furthermore,a new computer search criterion for a linear transformation matrix is also proposed. New search criterion is to minimize the symbol error rate based on OSIC detection. Computer simulations show that the performance of proposed LDCs transmission scheme is better than the original LDCs.展开更多
The weight hierarchy of a linear [n, k;q] code C over GF(q) is the sequence (d1,d2,..., dk) where dr is the size of the smallest support of an r-dimensional subcode of C. An [n,k;q] code satisfies the chain condition ...The weight hierarchy of a linear [n, k;q] code C over GF(q) is the sequence (d1,d2,..., dk) where dr is the size of the smallest support of an r-dimensional subcode of C. An [n,k;q] code satisfies the chain condition if there exists subcodes D1 D2 … Dk = C of C such that Dr has dimension r and support of size dr for all r. Further, C satisfies the almost chain condition if it does not satisfy the chain condition, but there exist subcodes Dr of dimension r and support of size dr for all r such that D2 D3 Dk = C and D1 D3. A simple necessary condition for a sequence to be the weight hierarchy of a code satisfying the almost chain condition is given. Further, explicit constructions of such codes are given, showing that in almost all cases, the necessary conditions are also sufficient.展开更多
The weight hierarchy of a [n, k; q] linear code C over Fq is the sequence （d1,…, dr,… , dk）, where dr is the smallest support weight of an r-dimensional subcode of C. In this paper, by using the finite projective ...The weight hierarchy of a [n, k; q] linear code C over Fq is the sequence （d1,…, dr,… , dk）, where dr is the smallest support weight of an r-dimensional subcode of C. In this paper, by using the finite projective geometry method, we research a class of weight hierarchy of linear codes with dimension 5. We first find some new pre- conditions of this class. Then we divide its weight hierarchies into six subclasses, and research one subclass to determine nearly all the weight hierarchies of this subclass of weight hierarchies of linear codes with dimension 5.展开更多
In this paper, we propose a novel space efficient secret sharing scheme on the basis of minimal linear codes, which satisfies the definition of a computationally efficient secret sharing scheme. In the scheme, we part...In this paper, we propose a novel space efficient secret sharing scheme on the basis of minimal linear codes, which satisfies the definition of a computationally efficient secret sharing scheme. In the scheme, we partition the underlying minimal linear code into disjoint classes, establishing a one-to-one correspondence between the minimal authorized subsets of participants and the representative codewords of all different classes. Each participant, with only one short share transmitted through a public channel, can share a large secret. Therefore, the proposed scheme can distribute a large secret in practical applications such as secure information dispersal in sensor networks and secure multiparty computation.展开更多
The maximum of g2-d2 for linear [n, k, d; q] codes C is studied. Here d2 is the smallest size of the support of 2-dimensional subcodes of C and g2 is the smallest size of the support of 2-dimensional subcodes of C whi...The maximum of g2-d2 for linear [n, k, d; q] codes C is studied. Here d2 is the smallest size of the support of 2-dimensional subcodes of C and g2 is the smallest size of the support of 2-dimensional subcodes of C which contains a codeword of weight d. The extra cost to the greedy adversary to get two symbols of information using some algorithm is g2-d2. For codes satisfying the fullrank condition of general dimensions, upper bounds on the maximum of g2-d2 are given. Under some condition we have got code C where g2-d2 reaches the upper bound.展开更多
The optimal and suboptimal structured algorithms of linear block codes from the geometrical perspective are represented.The minimum distance and weight property lemmas and the theorem are proved for the generator matr...The optimal and suboptimal structured algorithms of linear block codes from the geometrical perspective are represented.The minimum distance and weight property lemmas and the theorem are proved for the generator matrix.Based upon the property of generator matrix,the structured algorithms of linear block codes are demonstrated.Since the complexity of optimal structured algorithm is very high,the binary linear block codes is searched by using the suboptimal structured algorithm.The comparison with Bose-Chaudhuri-Hocquenqhem（BCH） codes shows that the searched linear block codes are equivalent on minimum distance and can be designed for more block lengths.Because the linear block codes are used widely in communication systems and digital applications,the optimal and suboptimal structured algorithms must have great future being widely used in many applications and perspectives.展开更多
This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block co...This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block code share the propertyof linear correlation, the existing linear correlation-basedidentification method is invalid for this case. This drawback can becircumvented by introducing a novel multi-fractal spectrum-basedmethod. Simulation results show that the new method has highrobustness and under the same conditions of bit error, the lowerthe code rate, the higher the recognition rate. Thus, the methodhas significant potential for future application in engineering.展开更多
A new architecture of space-time codes as a combination of orthogonal space-time block codes （OSTBC） and linear dispersion codes （LDC） is proposed in order to improve the bit error rate（BER） performance of OSTBC...A new architecture of space-time codes as a combination of orthogonal space-time block codes （OSTBC） and linear dispersion codes （LDC） is proposed in order to improve the bit error rate（BER） performance of OSTBC.The scheme proposed is named linear dispersion orthogonal space-time block codes （LDOSTBC）.In LDOSTBC scheme,firstly,the data is coded into LDC codewords.Then,the coded LDC substreams are coded into OSTBC codewords again.The decoding algorithm of LDOSTBC combines linear decoding of OSTBC and ML decoding or suboptimum detection algorithms of LDC.Compared with OSTBC scheme when the rate of LDC is MtR,the performance of LDOSTBC scheme can be improved without decreasing the data rate,where Mt is the number of transmit antennas and R is the spectral efficiency of the modulation constellation.If some rate penalty is allowed,when the rate of LDC is less than MtR the performance of LDOSTBC can be improved further.展开更多
The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general...The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general linear codes" is a basic theoretical issue and has important scientific significance in communication system.However,it is impossible for g-ary linear codes of dimension k when q and k are slightly larger,then a reasonable formulation of the problem is modified as: "Determine almost all weight hierarchies of general g-ary linear codes of dimension k".In this paper,based on the finite projective geometry method,the authors study g-ary linear codes of dimension 5 in class IV,and find new necessary conditions of their weight hierarchies,and classify their weight hierarchies into6 subclasses.The authors also develop and improve the method of the subspace set,thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV.It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes(classes III and VI),and break through the difficulties.Furthermore,the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough(not most tight nor best),so,it is important to excogitate further new necessary conditions for attacking and solving the fc-dimensional problem.展开更多
The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved i...The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with heuristic techniques such as genetic algorithms and local search algorithms. In this paper we propose two approaches to attack the hardness of this problem. The first approach is based on genetic algorithms and it yield to good results comparing to another work based also on genetic algorithms. The second approach is based on a new randomized algorithm which we call 'Multiple Impulse Method (MIM)', where the principle is to search codewords locally around the all-zero codeword perturbed by a minimum level of noise, anticipating that the resultant nearest nonzero codewords will most likely contain the minimum Hamming-weight codeword whose Hamming weight is equal to the minimum distance of the linear code.展开更多
In the Internet of vehicles(IoV),direct communication between vehicles,i.e.,vehicle-tovehicle(V2V)may have lower latency,compared to the schemes with help of Road Side Unit(RSU)or base station.In this paper,the scenar...In the Internet of vehicles(IoV),direct communication between vehicles,i.e.,vehicle-tovehicle(V2V)may have lower latency,compared to the schemes with help of Road Side Unit(RSU)or base station.In this paper,the scenario where the demands of a vehicle are satisfied by cooperative transmissions from those one in front is considered.Since the topology of the vehicle network is dynamic,random linear network coding is applied in such a multisource single-sink vehicle-to-vehicle network,where each vehicle is assumed to broadcast messages to others so that the intermediate vehicles between sources and sink can reduce the latency collaboratively.It is shown that the coding scheme can significantly reduce the time delay compared with the non-coding scheme even in the channels with high packet loss rate.In order to further optimize the coding scheme,one can increase the generation size,where the generation size means the number of raw data packets sent by the source node to the sink node in each round of communication.Under the premise of satisfying the coding validity,we can dynamically select the Galois field size according to the number of intermediate nodes.It is not surprised that the reduction in the Galois field size can further reduce the transmission latency.展开更多
文摘Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, we consider constructing binary linear codes by combining deep holes with binary BCH codes. In this article, we consider the 2-error-correcting binary primitive BCH codes and the extended codes to construct new binary linear codes by combining them with deep holes, respectively. Furthermore, three classes of binary linear codes are constructed, and then we determine the parameters and the weight distributions of these new binary linear codes.
基金She was with the Department of Mathematics in Wuhan University while writting this paper.
文摘Abraham Lempel et al made a connection between linear codes and systems of bilinear forms over finite fields. In this correspondence, a new simple proof of a theorem in [1] is presented; in addition, the encoding process and the decoding procedure of RS codes are simplified via circulant matrices. Finally, the results show that the correspondence between bilinear forms and linear codes is not unique.
文摘m-weight, as a new generalization of classical Hamming weight, was discussedin this paper. A condition for the existence of linear codes of certain m-weights was given; theSingleton bound, Plotkin bound and Sphere Parking bound of Hamming weight were correspondinglygeneralized to the m-weight.
文摘Secret sharing is an important topic in cryptography and has applications in information security. The coding theory has been an important role in the constructing of secret sharing schemes. It is known that every linear code can be used to construct secret sharing schemes. So, we use the parity-check matrix of a linear code to construct secret sharing schemes based on linear codes. We also describe some techniques to recover the secret and determine the access structure of the new scheme. In this paper, we use the Massey＇s secret sharing scheme.
基金Supported by the Scientific Research Foundation of Hubei Provincial Education Department of China(Q20174503)the National Science Foundation of Hubei Polytechnic University of China(12xjz14A and 17xjz03A)。
文摘In this paper,we first give the definition of the Euclidean sums of linear codes,and prove that the Euclidean sums of linear codes are Euclidean dual-containing.Then we construct two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of the Reed-Solomon codes,and two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of linear codes generated by Vandermonde matrices over finite fields.Moreover,these optimal asymmetric quantum errorcorrecting codes constructed in this paper are different from the ones in the literature.
基金supported by the Natural Science Foundation of China (No.11901062)the Sichuan Natural Science Foundation (No.2024NSFSC0417)。
文摘Recently,linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes,constant composition codes,strongly regular graphs and so on.In this paper,based on the Weil sums,several classes of two-weight or three-weight linear codes are presented by choosing a proper defining set,and their weight enumerators and complete weight enumerators are determined.Furthermore,these codes are proven to be minimal.By puncturing these linear codes,two classes of two-weight projective codes are obtained,and the parameters of the corresponding strongly regular graph are given.This paper generalizes the results of[7].
基金supported by National Natural Science Funds of China under Grant No.60973125College Doctoral Funds of China under Grant No.20080359003+1 种基金Anhui College Natural Science Research Project under Grant No.KJ2010B171Research Project of Hefei Normal University under Grant No.2012kj10
文摘In this paper, the MacWilliams type identity for the m-ply Lee weight enumerator for linear codes over F2 ＋uF2 is determined. As an application of this identity, the authors obtain a MacWilliams type identity on Lee weight for linear codes over F2m ＋ uF2m. Furthermore, the authors prove a duality for the m-ply Lee weight distributions by taking advantage of the Krawtchouk polynomials.
基金supported by the Natural Science Foundation of Hubei Province under Grant No.D20144401the Natural Science Foundation of Hubei Polytechnic University under Grant Nos.12xjz14A,11yjz37B
文摘The Lee weight enumerators and the complete weight enumerators for the linear codes over ring R = F2 ＋ u F2 ＋ v F2 are defined and Gray map from R^nto F2^3n is constructed. By proving the fact that the Gray images of the self-dual codes over R are the self-dual codes over F2, and based on the Mac Williams identities for the Hamming weight enumerators of linear codes over F2, the Mac Williams identities for Lee weight enumerators of linear codes over R are given. Further, by introducing a special variable t, the Mac Williams identities for the complete weight enumerators of linear codes over R are obtained. Finally, an example which illustrates the correctness and function of the two Mac Williams identities is provided.
基金The work was supported in part by the National Natural Science Foundation of China(Grant No.61872103)in part by Guangxi Science and Technology Foundation(Guike AB18281019,Guike AD18281026)+1 种基金in part by Guangxi Natural Science Foundation(2019GXNSFGA245004)in part by the Foundation of Ministry of Education Key Laboratory of Cognitive Radio and Information Processing(Guilin University of Electronic Technology)(CRKL180107).
文摘Highly nonlinear resilient functions play a crucial role in nonlinear combiners which are usual hardware oriented stream ciphers.During the past three decades,the main idea of construction of highly nonlinear resilient functions are benefited from concatenating a large number of affine subfunctions.However,these resilient functions as core component of ciphers usually suffered from the guess and determine attack or algebraic attack since the n-variable nonlinear Boolean functions can be easily given rise to partial linear relations by fixing at most nil variables of them.How to design highly nonlinear resilient functions(S-boxes)without concatenating a large number of nil variables affine subfunctions appears to be an important task.In this article,a new construction of highly nonlinear resilient functions is proposed.These functions consist of two classes subfunctions.More specially,the first class(nonlinear part)contains both the bent functions with 2k variables and some affine subfUnctions with n/2-k variables which are attained by using[n/2-k,m,d]disjoint linear codes.The second class(linear part)includes some linear subfunctions with nil variables which are attained by using[n/2,m,d]disjoint linear codes.It is illustrated that these resilient functions have high nonlinearity and high algebraic degree.In particular,It is different from previous well-known resilient S-boxes,these new S-boxes cannot be directly decomposed into some affine subftinctions with nil variables by fixing at most nil variables.It means that the S-boxes(vectorial Boolean functions)which use these resilient functions as component functions have more favourable cryptography properties against the guess and determine attack or algebraic attacks.
文摘Linear dispersion codes (LDCs) were originally designed based on maximum likelihood detection. They do not have good performance when using ordered successive interference cancellation (OSIC) detection. In this paper,we propose a new improved linear dispersion codes transmission scheme to combat performance loss of original LDCs when using OSIC detection. We introduce an interleaver to each data substream transmitted over different antennas after LDCs encoder. Furthermore,a new computer search criterion for a linear transformation matrix is also proposed. New search criterion is to minimize the symbol error rate based on OSIC detection. Computer simulations show that the performance of proposed LDCs transmission scheme is better than the original LDCs.
基金supported by the Norwegian Research Council and the National Natural Science Foundation of China(Grant No.10271116).
文摘The weight hierarchy of a linear [n, k;q] code C over GF(q) is the sequence (d1,d2,..., dk) where dr is the size of the smallest support of an r-dimensional subcode of C. An [n,k;q] code satisfies the chain condition if there exists subcodes D1 D2 … Dk = C of C such that Dr has dimension r and support of size dr for all r. Further, C satisfies the almost chain condition if it does not satisfy the chain condition, but there exist subcodes Dr of dimension r and support of size dr for all r such that D2 D3 Dk = C and D1 D3. A simple necessary condition for a sequence to be the weight hierarchy of a code satisfying the almost chain condition is given. Further, explicit constructions of such codes are given, showing that in almost all cases, the necessary conditions are also sufficient.
基金supported by the National Natural Science Foundation of China (Nos. 61303212 and 61170080)the State Key Program of the National Natural Science of China (Nos. 61332019 and U1135004)the Fundamental Research Funds for the Central Universities, South-Central University for Nationalities (No. CZY14019)
文摘The weight hierarchy of a [n, k; q] linear code C over Fq is the sequence （d1,…, dr,… , dk）, where dr is the smallest support weight of an r-dimensional subcode of C. In this paper, by using the finite projective geometry method, we research a class of weight hierarchy of linear codes with dimension 5. We first find some new pre- conditions of this class. Then we divide its weight hierarchies into six subclasses, and research one subclass to determine nearly all the weight hierarchies of this subclass of weight hierarchies of linear codes with dimension 5.
基金Supported by the National Natural Science Foundation of China (11271237)
文摘In this paper, we propose a novel space efficient secret sharing scheme on the basis of minimal linear codes, which satisfies the definition of a computationally efficient secret sharing scheme. In the scheme, we partition the underlying minimal linear code into disjoint classes, establishing a one-to-one correspondence between the minimal authorized subsets of participants and the representative codewords of all different classes. Each participant, with only one short share transmitted through a public channel, can share a large secret. Therefore, the proposed scheme can distribute a large secret in practical applications such as secure information dispersal in sensor networks and secure multiparty computation.
基金This paper was presented at International Congress of Mathematicians,August 20-28,2002,BeijingThis work was supported by the Norwegian Research Council and the National NaturalScience Foundation of China(GrantNo.10271116).
文摘The maximum of g2-d2 for linear [n, k, d; q] codes C is studied. Here d2 is the smallest size of the support of 2-dimensional subcodes of C and g2 is the smallest size of the support of 2-dimensional subcodes of C which contains a codeword of weight d. The extra cost to the greedy adversary to get two symbols of information using some algorithm is g2-d2. For codes satisfying the fullrank condition of general dimensions, upper bounds on the maximum of g2-d2 are given. Under some condition we have got code C where g2-d2 reaches the upper bound.
文摘The optimal and suboptimal structured algorithms of linear block codes from the geometrical perspective are represented.The minimum distance and weight property lemmas and the theorem are proved for the generator matrix.Based upon the property of generator matrix,the structured algorithms of linear block codes are demonstrated.Since the complexity of optimal structured algorithm is very high,the binary linear block codes is searched by using the suboptimal structured algorithm.The comparison with Bose-Chaudhuri-Hocquenqhem（BCH） codes shows that the searched linear block codes are equivalent on minimum distance and can be designed for more block lengths.Because the linear block codes are used widely in communication systems and digital applications,the optimal and suboptimal structured algorithms must have great future being widely used in many applications and perspectives.
基金supported by the National Natural Science Foundation of China(61171170) the Natural Science Foundation of Anhui Province(1408085QF115)
文摘This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block code share the propertyof linear correlation, the existing linear correlation-basedidentification method is invalid for this case. This drawback can becircumvented by introducing a novel multi-fractal spectrum-basedmethod. Simulation results show that the new method has highrobustness and under the same conditions of bit error, the lowerthe code rate, the higher the recognition rate. Thus, the methodhas significant potential for future application in engineering.
基金Sponsored by the "111" Project of China (B08038)Important National Science & Technology Specific Projects (2009ZX03003-003+2 种基金2009ZX03003-004) the NSFC-Guangdong (U0635003)Program for Changjiang Scholars and Innovative Research Team in University(IRT0852)
文摘A new architecture of space-time codes as a combination of orthogonal space-time block codes （OSTBC） and linear dispersion codes （LDC） is proposed in order to improve the bit error rate（BER） performance of OSTBC.The scheme proposed is named linear dispersion orthogonal space-time block codes （LDOSTBC）.In LDOSTBC scheme,firstly,the data is coded into LDC codewords.Then,the coded LDC substreams are coded into OSTBC codewords again.The decoding algorithm of LDOSTBC combines linear decoding of OSTBC and ML decoding or suboptimum detection algorithms of LDC.Compared with OSTBC scheme when the rate of LDC is MtR,the performance of LDOSTBC scheme can be improved without decreasing the data rate,where Mt is the number of transmit antennas and R is the spectral efficiency of the modulation constellation.If some rate penalty is allowed,when the rate of LDC is less than MtR the performance of LDOSTBC can be improved further.
基金supported by the National Natural Science Foundation of China under Grant No.11171366"the Fundamental Research Funds for the Central Universities"South-Central University for Nationalities under Grant No.CZY12014
文摘The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general linear codes" is a basic theoretical issue and has important scientific significance in communication system.However,it is impossible for g-ary linear codes of dimension k when q and k are slightly larger,then a reasonable formulation of the problem is modified as: "Determine almost all weight hierarchies of general g-ary linear codes of dimension k".In this paper,based on the finite projective geometry method,the authors study g-ary linear codes of dimension 5 in class IV,and find new necessary conditions of their weight hierarchies,and classify their weight hierarchies into6 subclasses.The authors also develop and improve the method of the subspace set,thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV.It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes(classes III and VI),and break through the difficulties.Furthermore,the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough(not most tight nor best),so,it is important to excogitate further new necessary conditions for attacking and solving the fc-dimensional problem.
文摘The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with heuristic techniques such as genetic algorithms and local search algorithms. In this paper we propose two approaches to attack the hardness of this problem. The first approach is based on genetic algorithms and it yield to good results comparing to another work based also on genetic algorithms. The second approach is based on a new randomized algorithm which we call 'Multiple Impulse Method (MIM)', where the principle is to search codewords locally around the all-zero codeword perturbed by a minimum level of noise, anticipating that the resultant nearest nonzero codewords will most likely contain the minimum Hamming-weight codeword whose Hamming weight is equal to the minimum distance of the linear code.
基金This work was supported in part by the Guangdong Basic and Applied Basic Research Foundation under Key Project 2019B1515120032in part by the National Science Foundation of China(NSFC)with grant no.61901534+3 种基金in part by the Science,Technology and Innovation Commission of Shenzhen Municipality with grant no.JCYJ20190807155617099in part by the University Basic Research Fund 20lgpy43in part by the Guangdong Natural Science Foundation of Grant No.2019A1515011622the Foundation of Grant No.2019-JCJQ-JJ-411.
文摘In the Internet of vehicles(IoV),direct communication between vehicles,i.e.,vehicle-tovehicle(V2V)may have lower latency,compared to the schemes with help of Road Side Unit(RSU)or base station.In this paper,the scenario where the demands of a vehicle are satisfied by cooperative transmissions from those one in front is considered.Since the topology of the vehicle network is dynamic,random linear network coding is applied in such a multisource single-sink vehicle-to-vehicle network,where each vehicle is assumed to broadcast messages to others so that the intermediate vehicles between sources and sink can reduce the latency collaboratively.It is shown that the coding scheme can significantly reduce the time delay compared with the non-coding scheme even in the channels with high packet loss rate.In order to further optimize the coding scheme,one can increase the generation size,where the generation size means the number of raw data packets sent by the source node to the sink node in each round of communication.Under the premise of satisfying the coding validity,we can dynamically select the Galois field size according to the number of intermediate nodes.It is not surprised that the reduction in the Galois field size can further reduce the transmission latency.
