Evaluation of the Hamming weights of a class of linear codes based on Gauss sums

被引：26
|
作者：
Heng, Ziling [1 ,2 ,3 ]
Yue, Qin [1 ,2 ,3 ]
机构：
[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 211100, Jiangsu, Peoples R China
[2] State Key Lab Cryptol, POB 5159, Beijing 100878, Peoples R China
[3] Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2017年 / 83卷 / 02期
基金：
中央高校基本科研业务费专项资金资助;
关键词：
Linear codes; Weight distribution; Gauss sums; Secret sharing schemes; IRREDUCIBLE CYCLIC CODES; SECRET SHARING SCHEMES; 2-WEIGHT; DISTRIBUTIONS;
D O I：
10.1007/s10623-016-0222-7
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Linear codes with a few weights have been widely investigated in recent years. In this paper, we mainly use Gauss sums to represent the Hamming weights of a class of q-ary linear codes under some certain conditions, where q is a power of a prime. The lower bound of its minimum Hamming distance is obtained. In some special cases, we evaluate the weight distributions of the linear codes by semi-primitive Gauss sums and obtain some one-weight, two-weight linear codes. It is quite interesting that we find new optimal codes achieving some bounds on linear codes. The linear codes in this paper can be used in secret sharing schemes, authentication codes and data storage systems.
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页码：307 / 326
页数：20
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