Several Constructions of Near MDS Codes and Optimal Locally Recoverable Codes

被引：0

作者：

Wang X.-R. ^{[1
]}

Heng Z.-L. ^{[1
]}

机构：

[1] School of Science, Chang'an University, Shaanxi, Xi'an

来源：

Tien Tzu Hsueh Pao/Acta Electronica Sinica | 2024年 / 52卷 / 03期

基金：

中国国家自然科学基金;

关键词：

distributed storage; locally recoverable code; near MDS code; weight distribution;

D O I：

10.12263/DZXB.20220634

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

Locally recoverable codes offer an efficient way to improve the repair efficiency of storage nodes by local recovery. They are widely used in distributed storage and cloud storage. In this paper, we first present several constructions of near MDS (near maximum distance separable) codes of dimension 4 or 5. The parameters and weight distributions of the codes are explicitly determined. In particular, some families of near MDS codes with the same parameters but different weight distributions are derived. Then the locality of the near MDS codes is also studied. Several families of distance-optimal and dimension-optimal locally recoverable codes are obtained. These locally recoverable codes have different parameters from those of known ones in the literature. © 2024 Chinese Institute of Electronics. All rights reserved.

引用

页码：957 / 966

页数：9

共 28 条

[1]

LI C J, YUE Q, LI F W., Weight distributions of cyclic codes with respect to pairwise coprime order elements, Finite Fields and Their Applications, 28, pp. 94-114, (2014)

[2]

DING C S., Designs from Linear Codes, (2019)

[3]

HENG Z L, DING C S, ZHOU Z C., Minimal linear codes over finite fields, Finite Fields and Their Applications, 54, pp. 176-196, (2018)

[4]

DU X N, LU H X, WANG R, Et al., A construction of two classes of linear codes with four-weights, Journal of Northwest Normal University (Natural Science), 54, 6, pp. 1-4, (2018)

[5]

YANG S D, YUE Q., Complete weight enumerators of a class of linear codes, Computer Engineering and Science, 41, 2, pp. 281-285, (2019)

[6]

YANG S D, YAO Z G., Complete weight enumerators of a family of three-weight linear codes, Designs, Codes and Cryptography, 82, 3, pp. 663-674, (2017)

[7]

DU X N, LI X D, LU H X, Et al., A construction of several classes of two-weight and three-weight linear codes, Journal of Northwest Normal University (Natural Science), 54, 2, pp. 30-35, (2018)

[8]

DU X N, LU H X, WANG R., Construction of a class of linear codes with four-weight and six-weight, Journal of Electronics & Information Technology, 41, 12, pp. 2995-2999, (2019)

[9]

YANG S D, TANG C M., The complete weight enumerator of cyclic codes, Journal of Jiangsu Normal University (Natural Science Edition), 36, 2, pp. 64-68, (2018)

[10]

HU L Q, YUE Q, ZHU X M., Weight distribution of cyclic codes with two non-zero points, Scientia Sinica (Mathematica), 44, 9, pp. 1021-1034, (2014)

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