Constructions of MDS, Near MDS and Almost MDS Codes From Cyclic Subgroups of F∗q2

Ziling Heng; Chengju Li; Xinran Wang

doi:10.1109/TIT.2022.3194914

Constructions of MDS, Near MDS and Almost MDS Codes From Cyclic Subgroups of F∗q²

Ziling Heng
, Chengju Li^*
, Xinran Wang

^*此作品的通讯作者

软件工程学院

Chang'an University
Southeast University, Nanjing

科研成果: 期刊稿件 › 文章 › 同行评审

23 引用（Scopus）

摘要

Linear codes achieving or nearly achieving the Singleton bound are interesting in both theory and practice. The objective of this paper is to construct several infinite families of MDS, near MDS and almost MDS codes from some special cyclic subgroups of Fq2∗. To this end, the augmentation and extension techniques are used. The codes in this paper have flexible parameters and their lengths could be large. The minimum linear locality of the codes constructed in this paper is also studied. Some infinite families of optimal linearly locally recoverable codes are obtained. Besides, some codes in this paper are proved to be proper for error detection.

源语言	英语
页（从-至）	7817-7831
页数	15
期刊	IEEE Transactions on Information Theory
卷	68
期	12
DOI	https://doi.org/10.1109/TIT.2022.3194914
出版状态	已出版 - 1 12月 2022

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abstract = "Linear codes achieving or nearly achieving the Singleton bound are interesting in both theory and practice. The objective of this paper is to construct several infinite families of MDS, near MDS and almost MDS codes from some special cyclic subgroups of Fq2∗. To this end, the augmentation and extension techniques are used. The codes in this paper have flexible parameters and their lengths could be large. The minimum linear locality of the codes constructed in this paper is also studied. Some infinite families of optimal linearly locally recoverable codes are obtained. Besides, some codes in this paper are proved to be proper for error detection.",

keywords = "MDS code, almost MDS code, locally recoverable code, near MDS code",

author = "Ziling Heng and Chengju Li and Xinran Wang",

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T1 - Constructions of MDS, Near MDS and Almost MDS Codes From Cyclic Subgroups of F∗q2

AU - Heng, Ziling

AU - Li, Chengju

AU - Wang, Xinran

PY - 2022/12/1

Y1 - 2022/12/1

N2 - Linear codes achieving or nearly achieving the Singleton bound are interesting in both theory and practice. The objective of this paper is to construct several infinite families of MDS, near MDS and almost MDS codes from some special cyclic subgroups of Fq2∗. To this end, the augmentation and extension techniques are used. The codes in this paper have flexible parameters and their lengths could be large. The minimum linear locality of the codes constructed in this paper is also studied. Some infinite families of optimal linearly locally recoverable codes are obtained. Besides, some codes in this paper are proved to be proper for error detection.

AB - Linear codes achieving or nearly achieving the Singleton bound are interesting in both theory and practice. The objective of this paper is to construct several infinite families of MDS, near MDS and almost MDS codes from some special cyclic subgroups of Fq2∗. To this end, the augmentation and extension techniques are used. The codes in this paper have flexible parameters and their lengths could be large. The minimum linear locality of the codes constructed in this paper is also studied. Some infinite families of optimal linearly locally recoverable codes are obtained. Besides, some codes in this paper are proved to be proper for error detection.

KW - MDS code

KW - almost MDS code

KW - locally recoverable code

KW - near MDS code

UR - https://www.scopus.com/pages/publications/85135741969

U2 - 10.1109/TIT.2022.3194914

DO - 10.1109/TIT.2022.3194914

M3 - 文章

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SN - 0018-9448

VL - 68

SP - 7817

EP - 7831

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 12

ER -

Constructions of MDS, Near MDS and Almost MDS Codes From Cyclic Subgroups of F∗q2

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Constructions of MDS, Near MDS and Almost MDS Codes From Cyclic Subgroups of F∗q²