Two families of optimal ternary cyclic codes with minimal distance four

被引：13

作者：

Zhao, Hai ^{[1
]}

Luo, Rong ^{[2
]}

Sun, Tongjun ^{[1
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

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

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2022年 / 79卷

关键词：

Cyclic codes; Linear codes; Optimal codes; Equations over finite fields;

D O I：

10.1016/j.ffa.2022.101995

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the two families of optimal ternary cyclic codes with parameters of [3(m) -1, 3(m) -1-2m, 4] are presented. Some conclusions proposed by Wang and Wu in 2016 are analyzed and refined, and the remaining problem in it is solved. In addition, a conjecture proposed by Ding and Helleseth in 2013 about a class of optimal ternary cyclic codes C-(l ,C- epsilon) in which e = (3(m-1) - 1)/2+ 3(h) + 1 with parameters [3(m) - 1,3(m) - 2m - 1, 4] is analyzed, where 0 <= h <= m - 1. (C) 2022 Elsevier Inc. All rights reserved.

引用

页数：17

共 20 条

[1] On almost perfect nonlinear functions over F2n [J].

Berger, Thierry P. ;

Canteaut, Anne ;

Charpin, Pascale ;

Laigle-Chapuy, Yann .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (09) :4160-4170

[2] Differential properties of power functions [J].

Blondeau, Celine ;

Canteaut, Anne ;

Charpin, Pascale .

2010 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, 2010, :2478-2482

[3] Linear codes from perfect nonlinear mappings and their secret sharing schemes [J].

Carlet, C ;

Ding, CS ;

Yuan, J .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2005, 51 (06) :2089-2102

[4]

Cary Huffman., 2003, Fundamentals of Error-Correcting Codes

[5] CYCLIC DECODING PROCEDURES FOR BOSE-CHAUDHURI-HOCQUENGHEM CODES [J].

CHIEN, RT .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1964, 10 (04) :357-&

[6] Optimal Ternary Cyclic Codes From Monomials [J].

Ding, Cunsheng ;

Helleseth, Tor .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2013, 59 (09) :5898-5904

[7] Hamming weights in irreducible cyclic codes [J].

Ding, Cunsheng ;

Yang, Jing .

DISCRETE MATHEMATICS, 2013, 313 (04) :434-446

[8] A q-polynomial approach to cyclic codes [J].

Ding, Cunsheng ;

Ling, San .

FINITE FIELDS AND THEIR APPLICATIONS, 2013, 20 :1-14

[9] ON DECODING BCH CODES [J].

FORNEY, GD .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1965, 11 (04) :549-557

[10] On an open problem about a class of optimal ternary cyclic codes [J].

Han, Dongchun ;

Yan, Haode .

FINITE FIELDS AND THEIR APPLICATIONS, 2019, 59 :335-343

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