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参数为[p^k,p^(k-1),p]和参数为[2p^k,p^(k-1)(p-1),d≤p]的循环码 被引量:1

Cyclic cides with parameters [p^k,p^(k-1),p] and [2p^k,p^(k-1)(p-1),d≤p]
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摘要 码的长度、维数以及码的极小距离是线性码的最主要的参数,其中,码的维数确定了码的大小,极小距离确定了码的纠错能力.在文献中已有关于二次剩余码和k次剩余码的一些结果.通过分析剩余码的特点,分别利用模pk及模2pk上原根的性质,构造了两类循环码,当p为奇素数,q为素数时,得到了一类参数为[pk,pk-1,p]的循环码,当p,q均为奇素数时,得到了一类参数为[2pk,pk-1(p-1),d≤p]的循环码,其中(p,q)=1. For linear coders,there are three major parameters,they are lengths of codes,dimensions of codes and minmum distances of codes.Dimensions of codes determine the numbers of codes and minimum distances of codes determine error correction ability.In literature there are some results on quadratic residue codes.In this paper,we construct a family of cyclic codes with parameters [p^k,p^k-1,p] and [2p^k,p^k-1(p-1),d≤p]by analyzing the characters of residue codes and using the primitive roots of modulo pk and modulo 2pk,where p is an odd prime.
出处 《辽宁师范大学学报(自然科学版)》 CAS 2009年第4期393-395,共3页 Journal of Liaoning Normal University:Natural Science Edition
关键词 原根 循环码 极小距离 primitive root: cyclic code minimum distance
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  • 1钟淑琴,马智,许亚杰.基于逻辑函数的量子纠错码构造[J].中国科学:信息科学,2010,40(2):249-257. 被引量:2
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  • 8钟淑琴,马智,许亚杰.基于矩阵方法的量子纠错码构造[J].计算机工程,2010,36(23):266-267. 被引量:2

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