Uniform Minors in Maximally Recoverable Codes

Matthias Grezet; Thomas Westerbäck; Ragnar Freij-Hollanti; Camilla Hollanti

doi:10.1109/LCOMM.2019.2921540

Uniform Minors in Maximally Recoverable Codes

Matthias Grezet, Thomas Westerbäck, Ragnar Freij-Hollanti, Camilla Hollanti

Matematiikan ja systeemianalyysin laitos

Mälardalen University

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

Abstrakti

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.

Alkuperäiskieli	Englanti
Sivut	1297-1300
Julkaisu	IEEE Communications Letters
Vuosikerta	23
Numero	8
DOI - pysyväislinkit	https://doi.org/10.1109/LCOMM.2019.2921540
Tila	Julkaistu - 7 kesäk. 2019
OKM-julkaisutyyppi	A1 Julkaistu artikkeli, soviteltu

Pääsy asiakirjaan

10.1109/LCOMM.2019.2921540

https://arxiv.org/abs/1906.02423

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title = "Uniform Minors in Maximally Recoverable Codes",

abstract = "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.",

keywords = "distributed storage, locally repairable codes, maximally recoverable codes, uniform minors, field size",

author = "Matthias Grezet and Thomas Westerb{\"a}ck and Ragnar Freij-Hollanti and Camilla Hollanti",

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AU - Grezet, Matthias

AU - Westerbäck, Thomas

AU - Freij-Hollanti, Ragnar

AU - Hollanti, Camilla

PY - 2019/6/7

Y1 - 2019/6/7

N2 - 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.

AB - 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.

KW - distributed storage

KW - locally repairable codes

KW - maximally recoverable codes

KW - uniform minors

KW - field size

U2 - 10.1109/LCOMM.2019.2921540

DO - 10.1109/LCOMM.2019.2921540

M3 - Article

SN - 1089-7798

VL - 23

SP - 1297

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JO - IEEE Communications Letters

JF - IEEE Communications Letters

IS - 8

ER -

Uniform Minors in Maximally Recoverable Codes

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