Non-existence of a ternary constant weight (16, 5, 15; 2048) diameter perfect code

Denis S. Krotov; Patric R J Östergård; Olli Pottonen

doi:10.3934/amc.2016013

Non-existence of a ternary constant weight (16, 5, 15; 2048) diameter perfect code

Denis S. Krotov, Patric R J Östergård, Olli Pottonen

Information Theory

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

3 Sitaatiot (Scopus)

Abstrakti

Ternary constant weight codes of length n = 2^m, weight n – 1, cardinality 2ⁿ and distance 5 are known to exist for every m for which there exists an APN permutation of order 2^m, that is, at least for all odd m ≥ 3 and for m = 6. We show the non-existence of such codes for m = 4 and prove that any codes with the parameters above are diameter perfect.

Alkuperäiskieli	Englanti
Sivut	393-399
Sivumäärä	7
Julkaisu	Advances in Mathematics of Communications
Vuosikerta	10
Numero	2
DOI - pysyväislinkit	https://doi.org/10.3934/amc.2016013
Tila	Julkaistu - 1 toukok. 2016
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

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10.3934/amc.2016013

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abstract = "Ternary constant weight codes of length n = 2m, weight n – 1, cardinality 2n and distance 5 are known to exist for every m for which there exists an APN permutation of order 2m, that is, at least for all odd m ≥ 3 and for m = 6. We show the non-existence of such codes for m = 4 and prove that any codes with the parameters above are diameter perfect.",

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author = "Krotov, {Denis S.} and {\"O}sterg{\aa}rd, {Patric R J} and Olli Pottonen",

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AU - Krotov, Denis S.

AU - Östergård, Patric R J

AU - Pottonen, Olli

PY - 2016/5/1

Y1 - 2016/5/1

N2 - Ternary constant weight codes of length n = 2m, weight n – 1, cardinality 2n and distance 5 are known to exist for every m for which there exists an APN permutation of order 2m, that is, at least for all odd m ≥ 3 and for m = 6. We show the non-existence of such codes for m = 4 and prove that any codes with the parameters above are diameter perfect.

AB - Ternary constant weight codes of length n = 2m, weight n – 1, cardinality 2n and distance 5 are known to exist for every m for which there exists an APN permutation of order 2m, that is, at least for all odd m ≥ 3 and for m = 6. We show the non-existence of such codes for m = 4 and prove that any codes with the parameters above are diameter perfect.

KW - Constant weight code

KW - Diameter perfect code

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DO - 10.3934/amc.2016013

M3 - Article

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JF - Advances in Mathematics of Communications

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ER -

Non-existence of a ternary constant weight (16, 5, 15; 2048) diameter perfect code

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