Two families of negacyclic BCH codes
Two families of negacyclic BCH codes
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DOI：
10.1007/s10623-023-01208-6
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发表时间：
2022-07
期刊：
影响因子：
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通讯作者：
Xiaoqiang Wang;Zhonghua Sun;C. Ding
中科院分区：
文献类型：
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作者：
Xiaoqiang Wang;Zhonghua Sun;C. Ding
负循环BCH码是负循环码的一个子类，在许多情况下是最好的线性码。然而，关于非循环BCH码的研究成果很少。设q为奇素数方幂，m为正整数.本文的目的是研究有限域上的非循环BCH码，并分析其参数。本文提出的双循环BCH码具有良好的参数，并且包含了许多最优线性码。对于一定的q和m，与相同维数和长度的循环码相比，本文所提出的非循环BCH码在某些情况下具有更大的最小距离。
Negacyclic BCH codes are a subclass of neagcyclic codes and are the best linear codes in many cases. However, there have been very few results on negacyclic BCH codes. Letqbe an odd prime power andmbe a positive integer. The objective of this paper is to study negacyclic BCH codes with lengthandover the finite fieldand analyse their parameters. The negacyclic BCH codes presented in this paper have good parameters in general, and contain many optimal linear codes. For certainqandm, compared with cyclic codes with the same dimension and length, the negacyclic BCH codes presented in this paper have a larger minimum distance in some cases.