有限域上一类极小线性码的构造  

A Construction of Minimal Linear Codes over Finite Fields

作　　者：代兴兴 陈文兵 DAI Xingxing;CHEN Wenbing(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2021年第3期32-36,共5页Journal of Anqing Normal University(Natural Science Edition)

摘　　要：极小线性码作为一类特殊的线性码,在信息共享和数据存储中有广泛的应用。本文首先介绍研究极小线性码所需要的基本概念和相关引理,然后在一类线性码中选取部分码字构成一类极小线性码,选取的极小线性码中所有非零码字的最小汉明重量和最大汉明重量的比值小于或等于(p-1)/p,其中p是奇素数。最后利用线性码上任意两个线性无关码字的汉明重量之间的关系证明构造的码是极小线性码,并给出构造的这个极小线性码的汉明重量分布。As a special kind of linear codes,minimal linear codes have widely used in information sharing and data storage.This paper first introduces the basic concepts and related lemmas needed to study minimal linear codes.Then,select some code words in this linear codes to form a minimal linear codes,and the ratio of the minimal Hamming weight to the maximum Hamming weight of all nonzero in the selected minimal linear codes is less than or equal to the ratio of p and p-1,where p is an odd prime number.Finally,by using the relationship between the Hamming weights of any two linearly independent code words,it is proved that the constructed code is a minimal linear code,and the Hamming weight distribution of the constructed minimal linear code is given.

关 键 词：线性码 线性最小码 迹函数 有限域 

分 类 号：O157.4[理学—数学]