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

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 $m\ge 3$ 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.

9 pages. Submitted for publication

References in corpus (1)

• The Perfect Binary One-Error-Correcting Codes of Length 15: Part I--Classification

Cited by in corpus (1)

• A family of diameter perfect constant-weight codes from Steiner systems