CONSTRUCTIONS OF SEVERAL FAMILIES OF MDS CODES AND NMDS CODES

被引：0

作者：

Yin, Yanan ^{[1
]}

Yan, Haode ^{[1
]}

机构：

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

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2024年

基金：

中国国家自然科学基金;

关键词：

Linear code; MDS code; NMDS code; t-design; WEIGHT DISTRIBUTIONS; INFINITE FAMILIES; CYCLIC CODES;

D O I：

10.3934/amc.2024051

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Linear codes achieving or nearly achieving the Singleton bound have many nice applications in data storage, combinatorial design, secret sharing, and so on. In this paper, we present several classes of MDS codes and NMDS codes, and the parameters of these codes are determined. In addition, by applying a result proposed by Tang and Ding (IEEE Trans. Inform. Theory, 67 (1), 244-254, 2021), we prove that some of these NMDS codes support t-designs, where t = 2 , 3. The parameters of these t-designs are also derived.

引用

页码：1222 / 1247

页数：26

共 34 条

[1] [Anonymous], 1999, Reed-Solomon Codes and Their Applications
[2] Ding C., 2022, DESIGNS LINEAR CODES, V2nd
[3] Infinite Families of Near MDS Codes Holding t-Designs
Ding, Cunsheng
Tang, Chunming
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2020, 66 (09) : 5419 - 5428
[4] An Infinite Family of Steiner Systems S(2,4,2m) from Cyclic Codes
Ding, Cunsheng
[J]. JOURNAL OF COMBINATORIAL DESIGNS, 2018, 26 (03) : 127 - 144
[5] Infinite families of 2-designs and 3-designs from linear codes
Ding, Cunsheng
Li, Chengju
[J]. DISCRETE MATHEMATICS, 2017, 340 (10) : 2415 - 2431
[6] Dinh H.Q., 2015, J ALGEBR COMB DISCRE, V2, P39
[7] Codes of Small Defect
Faldum A.
Willems W.
[J]. Designs, Codes and Cryptography, 1997, 10 (3) : 341 - 350
[8] GOLAY MJE, 1949, P IRE, V37, P657
[9] New infinite families of near MDS codes holding t-designs
Heng, Ziling
Wang, Xinran
[J]. DISCRETE MATHEMATICS, 2023, 346 (10)
[10] Constructions of cyclic codes and extended primitive cyclic codes with their applications
Heng, Ziling
Wang, Xinran
Li, Xiaoru
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2023, 89

← 1 2 3 4 →