The Weight Distributions of Two Classes of Linear Codes From Perfect Nonlinear Functions

被引：0

作者：

Wu, Huawei ^{[1
]}

Yang, Jing ^{[1
]}

Feng, Keqin ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2024年 / 70卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Bent functions; exponential sums; group actions; linear codes; minimum distance; perfect nonlinear; value distribution; Walsh transform; weakly regular bent; weight distribution;

D O I：

10.1109/TIT.2023.3348228

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we employ general results on the value distributions of perfect nonlinear functions from F-p(m) to F-p to give a unified approach to determining the weight distributions of two classes of linear codes over F-p constructed from perfect nonlinear functions, where p is an odd prime and m is an odd number. When m is even, we give some mild additional conditions for similar conclusions to hold.

引用

页码：4102 / 4109

页数：8

共 50 条

[31] The weight distributions of two classes of p-ary cyclic codes [J].

Zheng, Dabin ;

Wang, Xiaoqiang ;

Hu, Lei ;

Zeng, Xiangyong .

FINITE FIELDS AND THEIR APPLICATIONS, 2014, 29 :202-224

[32] The Weight Distributions of Two Classes of Nonbinary Cyclic Codes With Few Weights [J].

Liu, Li ;

Xie, Xianhong ;

Li, Lanqiang ;

Zhu, Shixin .

IEEE COMMUNICATIONS LETTERS, 2017, 21 (11) :2336-2339

[33] The weight distributions of cyclic codes with two zeros and zeta functions [J].

Boston, Nigel ;

McGuire, Gary .

JOURNAL OF SYMBOLIC COMPUTATION, 2010, 45 (07) :723-733

[34] Weight Distributions of Two Classes of Cyclic Codes With Respect to Two Distinct Order Elements [J].

Li, Chengju ;

Yue, Qin .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2014, 60 (01) :296-303

[35] Two classes of 2-weight and 3-weight linear codes in terms of Kloosterman sums [J].

Xiaoshan Quan ;

Qin Yue ;

Xia Li ;

Chengju Li .

Cryptography and Communications, 2023, 15 :365-380

[36] Several classes of binary linear codes and their weight enumerators [J].

Li, Fei ;

Yan, Yang ;

Wang, Qiuyan ;

Yan, Tongjiang .

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2019, 30 (02) :93-106

[37] Value Distributions of Perfect Nonlinear Functions [J].

Lukas Kölsch ;

Alexandr Polujan .

Combinatorica, 2024, 44 :231-268

[38] Complete weight enumerators of two classes of linear codes with a few weights [J].

Qi, Minglong ;

Xiong, Shengwu .

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2021, 32 (01) :63-79

[39] Complete weight enumerators of two classes of linear codes with a few weights [J].

Minglong Qi ;

Shengwu Xiong .

Applicable Algebra in Engineering, Communication and Computing, 2021, 32 :63-79

[40] A construction of several classes of two-weight and three-weight linear codes [J].

Chengju Li ;

Qin Yue ;

Fang-Wei Fu .

Applicable Algebra in Engineering, Communication and Computing, 2017, 28 :11-30

← 1 2 3 4 5 →