On binary matroid minors and applications to data storage over small fields

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

*Tämän työn vastaava kirjoittaja

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussaConference article in proceedingsScientificvertaisarvioitu

1 Sitaatiot (Scopus)

Abstrakti

Locally repairable codes for distributed storage systems have gained a lot of interest recently, and various constructions can be found in the literature. However, most of the constructions result in either large field sizes and hence too high computational complexity for practical implementation, or in low rates translating into waste of the available storage space. In this paper we address this issue by developing theory towards code existence and design over a given field. This is done via exploiting recently established connections between linear locally repairable codes and matroids, and using matroid-theoretic characterisations of linearity over small fields. In particular, nonexistence can be shown by finding certain forbidden uniform minors within the lattice of cyclic flats. It is shown that the lattice of cyclic flats of binary matroids have additional structure that significantly restricts the possible locality properties of F2-linear storage codes. Moreover, a collection of criteria for detecting uniform minors from the lattice of cyclic flats of a given matroid is given, which is interesting in its own right.

AlkuperäiskieliEnglanti
OtsikkoCoding Theory and Applications
Alaotsikko5th International Castle Meeting, ICMCTA 2017, Vihula, Estonia, August 28-31, 2017, Proceedings
KustantajaSpringer
Sivut139-153
Sivumäärä15
ISBN (painettu)9783319662770
DOI - pysyväislinkit
TilaJulkaistu - 2017
OKM-julkaisutyyppiA4 Artikkeli konferenssijulkaisussa
TapahtumaInternational Castle Meeting on Coding Theory and Applications - Vihula, Viro
Kesto: 28 elok. 201731 elok. 2017
Konferenssinumero: 5

Julkaisusarja

NimiLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
KustantajaSpringer
Vuosikerta10495 LNCS
ISSN (painettu)0302-9743
ISSN (elektroninen)1611-3349

Conference

ConferenceInternational Castle Meeting on Coding Theory and Applications
LyhennettäICMCTA
Maa/AlueViro
KaupunkiVihula
Ajanjakso28/08/201731/08/2017

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