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

Article Contents

2016, Volume 10, Issue 2: 393-399. Doi: 10.3934/amc.2016013

This issue Previous Article Codes over local rings of order 16 and binary codes Next Article Nearly perfect sequences with arbitrary out-of-phase autocorrelation

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

1.
Sobolev Institute of Mathematics, Mechanics and Mathematics Department, Novosibirsk State University, Novosibirsk
2.
Department of Communications and Networking, School of Electrical Engineering, Aalto University, P.O. Box 13000, 00076 Aalto
3.
School of Mathematics and Physics, The University of Queensland, Brisbane

Received: July 31, 2014

Revised: November 30, 2014

Published: April 2016

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Abstract

Ternary constant weight codes of length $n=2^m$, weight $n-1$, cardinality $2^n$ 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 $m \geq 3$ 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.

Keywords:

Constant weight code,
diameter perfect code.

Mathematics Subject Classification: Primary: 94B25.

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References

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