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

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

Journal

Advances in Mathematics of Communications
ISSN: 1930-5346 , E-ISSN: 1930-5338

Output data

Year: 2016, Volume: 10, Number: 2, Pages: 393-399 Pages count : 7 DOI: 10.3934/amc.2016013

Tags

diameter perfect code., Constant weight code

Authors

Krotov D. ^1,2 , Östergård P.R.J. ³ , Pottonen O. ⁴

Affiliations

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

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.

Krotov D. , Östergård P.R.J. , Pottonen O.
Non-existence of a ternary constant weight (16,5,15;2048) diameter perfect code
Advances in Mathematics of Communications. 2016. V.10. N2. P.393-399. DOI: 10.3934/amc.2016013 WOS Scopus РИНЦ OpenAlex

Submitted:	Aug 31, 2014
Published print:	May 1, 2016

Web of science:	WOS:000377602300013
Scopus:	2-s2.0-84964786809
Elibrary:	27151577
OpenAlex:	W3098064218

DB	Citing
Web of science	2
Scopus	3
OpenAlex	1