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

Information Theory

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

6 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 elok. 2016
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

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10.3934/amc.2016020

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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",

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doi = "10.3934/amc.2016020",

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T1 - Further results on the classification of MDS codes

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AU - Östergård, Patric R J

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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

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DO - 10.3934/amc.2016020

M3 - Article

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VL - 10

SP - 489

EP - 498

JO - Advances in Mathematics of Communications

JF - Advances in Mathematics of Communications

IS - 3

ER -

Further results on the classification of MDS codes

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