Uniform Minors in Maximally Recoverable Codes

被引：3

作者：

Grezet, Matthias ^{[1
]}

Westerback, Thomas ^{[2
]}

Freij-Hollanti, Ragnar ^{[1
]}

Hollanti, Camilla ^{[1
]}

机构：

[1] Aalto Univ, Dept Math & Syst Anal, Aalto 00076, Finland

[2] Malardanen Univ, Div Appl Math, UKK, S-72123 Vasteras, Sweden

来源：

IEEE COMMUNICATIONS LETTERS | 2019年 / 23卷 / 08期

基金：

芬兰科学院;

关键词：

Distributed storage; locally repairable codes; maximally recoverable codes; uniform minors; field size;

D O I：

10.1109/LCOMM.2019.2921540

中图分类号：

TN [电子技术、通信技术];

学科分类号：

0809 ;

摘要：

In this letter, locally recoverable codes with maximal recoverability are studied with a focus on identifying the MDS codes resulting from puncturing and shortening. By using matroid theory and the relation between MDS codes and uniform minors, the list of all the possible uniform minors is derived. This list is used to improve the known non-asymptotic lower bound on the required field size of a maximally recoverable code.

引用

页码：1297 / 1300

页数：4

共 50 条

[41] Locally maximal recoverable codes and LMR-LCD codes
Rajpurohit, Rajendra Prasad
Bhaintwal, Maheshanand
Rajput, Charul
[J]. DESIGNS CODES AND CRYPTOGRAPHY, 2024, 92 (10) : 2881 - 2899
[42] Calculating recoverable reserves with uniform conditioning
Neufeld, C
Deutsch, C
[J]. GIS AND SPATIAL ANALYSIS, VOL 1AND 2, 2005, : 1065 - 1070
[43] UNIFORM CODES
MASSEY, JL
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1966, 12 (02) : 132 - +
[44] Several Constructions of Near MDS Codes and Optimal Locally Recoverable Codes
Wang, Xin-Ran
Heng, Zi-Ling
[J]. Tien Tzu Hsueh Pao/Acta Electronica Sinica, 2024, 52 (03): : 957 - 966
[45] Constructions of near MDS codes which are optimal locally recoverable codes
Li, Xiaoru
Heng, Ziling
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2023, 88
[46] Near MDS Codes with Dimension 4 and Their Application in Locally Recoverable Codes
Heng, Ziling
Li, Xiaoru
[J]. ARITHMETIC OF FINITE FIELDS, WAIFI 2022, 2023, 13638 : 142 - 158
[47] A Partition of the Hypercube into Maximally Nonparallel Hamming Codes
Krotov, Denis S.
[J]. JOURNAL OF COMBINATORIAL DESIGNS, 2014, 22 (04) : 179 - 187
[48] Locally Recoverable Codes Over Zp s
Kourani, Nasim Abdi
Khodaiemehr, Hassan
Nikmehr, Mohammad Javad
[J]. IEEE TRANSACTIONS ON COMMUNICATIONS, 2024, 72 (05) : 2503 - 2518
[49] Monomial-Cartesian codes and their duals, with applications to LCD codes, quantum codes, and locally recoverable codes
Lopez, Hiram H.
Matthews, Gretchen L.
Soprunov, Ivan
[J]. DESIGNS CODES AND CRYPTOGRAPHY, 2020, 88 (08) : 1673 - 1685
[50] Monomial-Cartesian codes and their duals, with applications to LCD codes, quantum codes, and locally recoverable codes
Hiram H. López
Gretchen L. Matthews
Ivan Soprunov
[J]. Designs, Codes and Cryptography, 2020, 88 : 1673 - 1685

← 1 2 3 4 5 →