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

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  • 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.
    Mathematics Subject Classification: Primary: 94B25.


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