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

Research output: Contribution to journal › Article › Scientific › peer-review

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	393-399
Number of pages	7
Journal	Advances in Mathematics of Communications
Volume	10
Issue number	2
DOIs	https://doi.org/10.3934/amc.2016013
Publication status	Published - 1 May 2016
MoE publication type	A1 Journal article-refereed

Keywords

Constant weight code
Diameter perfect code

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10.3934/amc.2016013

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

Abstract

Keywords

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