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

^*Corresponding author for this work

Software Engineering Institute

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

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.

Original language	English
Pages (from-to)	7817-7831
Number of pages	15
Journal	IEEE Transactions on Information Theory
Volume	68
Issue number	12
DOIs	https://doi.org/10.1109/TIT.2022.3194914
State	Published - 1 Dec 2022

Keywords

MDS code
almost MDS code
locally recoverable code
near MDS code

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10.1109/TIT.2022.3194914

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

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

AN - SCOPUS:85135741969

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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Keywords

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