Further results on the classification of MDS codes

Janne I. Kokkala; Patric R J Östergård

doi:10.3934/amc.2016020

Further results on the classification of MDS codes

Janne I. Kokkala, Patric R J Östergård

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

2 Sitaatiot (Scopus)

Abstrakti

An unrestricted q-ary maximum distance separable (MDS) code C with length n over an alphabet A (of size q) is a set of q^k codewords that are elements of Aⁿ, such that the smallest Hamming distance between two distinct codewords in C is d = n ̶ k + 1. Sets of mutually orthogonal Latin squares of orders q ≤ 9, corresponding to q-ary MDS codes of size q², and q-ary one-error-correcting MDS codes for q ≤ 8 have been classified in earlier studies. These results are used here to complete the classification of all 7-ary and 8-ary MDS codes with d ≥ 3 using a computer search.

Alkuperäiskieli	Englanti
Sivut	489-498
Sivumäärä	10
Julkaisu	Advances in Mathematics of Communications
Vuosikerta	10
Numero	3
DOI - pysyväislinkit	https://doi.org/10.3934/amc.2016020
Tila	Julkaistu - 1 elokuuta 2016
OKM-julkaisutyyppi	A1 Julkaistu artikkeli, soviteltu

Pääsy asiakirjaan

10.3934/amc.2016020

Muut tiedostot ja linkit

Link to publication in Scopus

Siteeraa tätä

@article{929ee94c2bec4ddd882b4eaedf35c372,

title = "Further results on the classification of MDS codes",

abstract = "An unrestricted q-ary maximum distance separable (MDS) code C with length n over an alphabet A (of size q) is a set of qk codewords that are elements of An, such that the smallest Hamming distance between two distinct codewords in C is d = n ̶ k + 1. Sets of mutually orthogonal Latin squares of orders q ≤ 9, corresponding to q-ary MDS codes of size q2, and q-ary one-error-correcting MDS codes for q ≤ 8 have been classified in earlier studies. These results are used here to complete the classification of all 7-ary and 8-ary MDS codes with d ≥ 3 using a computer search.",

keywords = "Classification, Latin hypercube, MDS code",

author = "Kokkala, {Janne I.} and {\"O}sterg{\aa}rd, {Patric R J}",

year = "2016",

month = aug,

day = "1",

doi = "10.3934/amc.2016020",

language = "English",

volume = "10",

pages = "489--498",

journal = "Advances in Mathematics of Communications ",

issn = "1930-5346",

number = "3",

}

TY - JOUR

T1 - Further results on the classification of MDS codes

AU - Kokkala, Janne I.

AU - Östergård, Patric R J

PY - 2016/8/1

Y1 - 2016/8/1

N2 - An unrestricted q-ary maximum distance separable (MDS) code C with length n over an alphabet A (of size q) is a set of qk codewords that are elements of An, such that the smallest Hamming distance between two distinct codewords in C is d = n ̶ k + 1. Sets of mutually orthogonal Latin squares of orders q ≤ 9, corresponding to q-ary MDS codes of size q2, and q-ary one-error-correcting MDS codes for q ≤ 8 have been classified in earlier studies. These results are used here to complete the classification of all 7-ary and 8-ary MDS codes with d ≥ 3 using a computer search.

AB - An unrestricted q-ary maximum distance separable (MDS) code C with length n over an alphabet A (of size q) is a set of qk codewords that are elements of An, such that the smallest Hamming distance between two distinct codewords in C is d = n ̶ k + 1. Sets of mutually orthogonal Latin squares of orders q ≤ 9, corresponding to q-ary MDS codes of size q2, and q-ary one-error-correcting MDS codes for q ≤ 8 have been classified in earlier studies. These results are used here to complete the classification of all 7-ary and 8-ary MDS codes with d ≥ 3 using a computer search.

KW - Classification

KW - Latin hypercube

KW - MDS code

UR - http://www.scopus.com/inward/record.url?scp=84980729623&partnerID=8YFLogxK

U2 - 10.3934/amc.2016020

DO - 10.3934/amc.2016020

M3 - Article

VL - 10

SP - 489

EP - 498

JO - Advances in Mathematics of Communications

JF - Advances in Mathematics of Communications

SN - 1930-5346

IS - 3

ER -

Further results on the classification of MDS codes

Abstrakti

Pääsy asiakirjaan

Muut tiedostot ja linkit

Sormenjälki

Siteeraa tätä