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

共 50 条

[21] On the covering radii of a class of binary primitive cyclic codes
Tutdere, Seher
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2022, 51 (01): : 20 - 26
[22] Several families of binary cyclic codes with good parameters
Sun, Zhonghua
FINITE FIELDS AND THEIR APPLICATIONS, 2023, 89
[23] An Infinite Family of Binary Cyclic Codes With Best Parameters
Sun, Zhonghua
Li, Chengju
Ding, Cunsheng
IEEE TRANSACTIONS ON INFORMATION THEORY, 2024, 70 (04) : 2411 - 2418
[24] On optimal parameters of a class of superimposed codes and designs
D'yachkov, AG
Macula, AJ
Rykov, VV
1998 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY - PROCEEDINGS, 1998, : 363 - 363
[25] On a Conjecture about a Class of Optimal Ternary Cyclic Codes
Li, Nian
Zhou, Zhengchun
Helleseth, Tor
2015 SEVENTH INTERNATIONAL WORKSHOP ON SIGNAL DESIGN AND ITS APPLICATIONS IN COMMUNICATIONS (IWSDA), 2015, : 57 - 60
[26] A LARGE CLASS OF CYCLIC AND SHORTENED CYCLIC BINARY CODES FOR MULTIPLE ERROR CORRECTION
HSU, HT
INFORMATION AND CONTROL, 1970, 16 (03): : 231 - &
[27] Five infinite families of binary cyclic codes and their related codes with good parameters
Liu, Hai
Li, Chengju
Ding, Cunsheng
FINITE FIELDS AND THEIR APPLICATIONS, 2023, 91
[28] Optimal generator matrices of binary cyclic codes over the binary symmetric channel
Chen, Houshou
2007 ASIA-PACIFIC CONFERENCE ON COMMUNICATIONS, 2007, : 405 - 408
[29] A new class of optimal linear codes with flexible parameters
Luo, Gaojun
Cao, Xiwang
Xu, Guangkui
Xu, Shanding
DISCRETE APPLIED MATHEMATICS, 2018, 237 : 126 - 131
[30] On an open problem about a class of optimal ternary cyclic codes
Han, Dongchun
Yan, Haode
FINITE FIELDS AND THEIR APPLICATIONS, 2019, 59 : 335 - 343

← 1 2 3 4 5 →