A class of binary cyclic codes with optimal parameters

被引：0

作者：

Liu, Kaiqiang ^{[1
,2
]}

Wang, Qi ^{[3
]}

Yan, Haode ^{[1
]}

机构：

[1] Southwest Jiaotong Univ, Sch Math, Chengdu 610031, Peoples R China

[2] State Key Lab Cryptol, POB 5159, Beijing 100878, Peoples R China

[3] Southern Univ Sci & Technol, Natl Ctr Appl Math Shenzhen, Dept Comp Sci & Engn, Shenzhen 518055, Peoples R China

来源：

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2022年 / 14卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Cyclic code; Binary code; Kloosterman sum; Gaussian period; Weight distribution; CONSTRUCTION; SEQUENCES; WEIGHTS;

D O I：

10.1007/s12095-021-00548-1

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

For positive integers k >= 2 and t, let m = 2kt and alpha be a primitive element of the finite field F-2m. In this paper, we study the parameters of a class of cyclic codes C-(1,C-v) which has two zeros alpha and alpha(v) with v = 2(m)-1/2(t)+1 It is shown that C-(1,C-v) is optimal or almost optimal with respect to the sphere packing bound. Based on some results of Kloosterman sums and Gaussian periods, the weight distribution of the dual code of C-(1,C-v) is completely determined when t = 5.

引用

页码：663 / 675

页数：13

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