论文标题
两个NegacyClic BCH代码的家族
Two families of negacyclic BCH codes
论文作者
论文摘要
NegacyClic BCH代码是Neagcyclic代码的子类，在许多情况下是最好的线性代码。但是，关于NegacyClic BCH代码的结果很少。让$ q $是奇怪的素数，$ m $是一个正整数。本文的目的是研究具有长度$ \ frac {q^m-1} {2} $和$ \ frac {q^m+1} {2} $的NegacyClic BCH代码，上面是有限字段$ \ mathbf（q）$ $。本文中介绍的NegacyClic BCH代码通常具有良好的参数，并且包含许多最佳线性代码。对于某些$ q $和$ m $，与具有相同尺寸和长度的循环代码相比，本文中介绍的NegacyClic BCH代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. Let $q$ be an odd prime power and $m$ be a positive integer. The objective of this paper is to study negacyclic BCH codes with length $\frac{q^m-1}{2}$ and $\frac{q^m+1}{2}$ over the finite field $\mathbf(q)$ and analyse their parameters. The negacyclic BCH codes presented in this paper have good parameters in general, and contain many optimal linear codes. For certain $q$ and $m$, 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.
