一类基于Weil和的少重量二元线性码  

A classes of few-weight binary linear codes from Weil sums

作　　者：冉晓琼 罗荣[1] RAN Xiaoqiong;LUO Rong(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,四川成都611756

出　　处：《湖北大学学报（自然科学版）》2024年第6期762-773,共12页Journal of Hubei University：Natural Science

基　　金：国家自然科学基金(201109574)资助。

摘　　要：近年来,通过定义集构造有限域上少重量线性码得到了广泛的关注。部分少重量线性码已经被应用于密钥分享方案,强正则图、认证码和关联方案。本文中研究一类线性码的参数和重量分布,得到二重或四重的二元线性码,并确定它们对偶码的参数。特别地,部分对偶码是关于Sphere packing界距离最优的。In past few years,constructing linear codes with a few weights by defining sets over finite fields had attracted a lot of attention.Some of these codes had been applied to secrete sharing,strongly regular graphs,authentication codes and association schemes.This paper investigated the parameters and weight distribution of a class of linear codes.Binary linear codes with two or four weights were derived and the parameters of their duals were also determined.Specifically,some of the dual codes were distance optimal with respect to the Sphere-packing bound.

关 键 词：线性码 重量分布 Weil和 Sphere packing界 

分 类 号：O157.4[理学—数学] O236.2[理学—基础数学]