New classes of optimal p-ary cyclic codes with minimum distance four

被引：0

作者：

Zha, Zhengbang ^{[1
]}

Hu, Lei ^{[2
]}

Wu, Gaofei ^{[3
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

[2] Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100085, Peoples R China

[3] Xidian Univ, Sch Cyber Engn, State Key Lab Integrated Serv Networks, Xian 710071, Peoples R China

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2025年 / 103卷

基金：

中国国家自然科学基金;

关键词：

Finite field; Cyclic code; Minimum distance;

D O I：

10.1016/j.ffa.2025.102588

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let C(1,e,s) denote the p-ary cyclic code with three zeros. In this paper, we present six classes of optimal p-ary cyclic codes C(1,e,s) with parameters [pn- 1, pn- 2n - 2,4] by using the quadratic and quartic characters on finite fields. In addition, we propose a class of optimal quinary cyclic codes by determining the solutions of equations over F5n . (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页数：18

共 20 条

[1]

[Anonymous], Greatest common divisors of am 1 and an 1

[2] 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

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

Ding, Cunsheng ;

Helleseth, Tor .

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

[4] A class of optimal ternary cyclic codes and their duals [J].

Fan, Cuiling ;

Li, Nian ;

Zhou, Zhengchun .

FINITE FIELDS AND THEIR APPLICATIONS, 2016, 37 :193-202

[5] Optimal Quinary Cyclic Codes with Minimum Distance Four [J].

Fan Jinmei ;

Zhang Yanhai .

CHINESE JOURNAL OF ELECTRONICS, 2020, 29 (03) :515-524

[6] 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

[7]

Huffman W., 2003, FUNDAMENTALS ERROR C

[8] Optimal ternary cyclic codes with minimum distance four and five [J].

Li, Nian ;

Li, Chunlei ;

Helleseth, Tor ;

Ding, Cunsheng ;

Tang, Xiaohu .

FINITE FIELDS AND THEIR APPLICATIONS, 2014, 30 :100-120

[9]

Lidl R., 1997, FINITE FIELDS

[10] Three new classes of optimal quinary cyclic codes with minimum distance four [J].

Liu, Yan ;

Cao, Xiwang .

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2025, 36 (03) :493-501

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