New infinite families of near MDS codes holding t-designs

被引：10

作者：

Heng, Ziling ^{[1
]}

Wang, Xinran ^{[1
]}

机构：

[1] Changan Univ, Sch Sci, Xian 710064, Peoples R China

来源：

DISCRETE MATHEMATICS | 2023年 / 346卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Linear code; Weight enumerator; t-design; LINEAR CODES; 3-DESIGNS;

D O I：

10.1016/j.disc.2023.113538

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In "Infinite families of near MDS codes holding t-designs, IEEE Trans. Inform. Theory, 2020, 66(9), pp. 5419-5428", Ding and Tang made a breakthrough in constructing the first two infinite families of NMDS codes holding 2-designs or 3-designs. Up to now, there are only a few known infinite families of NMDS codes holding t-designs in the literature. The objective of this paper is to construct new infinite families of NMDS codes holding t-designs. We determine the weight enumerators of the NMDS codes and prove that the NMDS codes hold 2-designs or 3-designs. Compared with known t-designs from NMDS codes, ours have different parameters. Besides, several infinite families of optimal locally recoverable codes are also derived via the NMDS codes.& COPY; 2023 Elsevier B.V. All rights reserved.

引用

页数：25

共 39 条

[1]

Cadambe V, 2013, INT SYMP NETW COD

[2]

Ding C., 2022, Designs from Linear Codes

[3]

Ding C., 2015, Codes From Difference Sets

[4] Infinite Families of Near MDS Codes Holding t-Designs [J].