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Trifferent codes with small lengths

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arxiv 2310.13563 v1 pith:4HLNQJWB submitted 2023-10-20 math.CO cs.DM

classification math.COcs.DM
keywords codestrifferentcardinalitylengthmaximumthereattainingcalled
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

A code $C \subseteq \{0, 1, 2\}^n$ of length $n$ is called trifferent if for any three distinct elements of $C$ there exists a coordinate in which they all differ. By $T(n)$ we denote the maximum cardinality of trifferent codes with length. $T(5)=10$ and $T(6)=13$ were recently determined. Here we determine $T(7)=16$, $T(8)=20$, and $T(9)=27$. For the latter case $n=9$ there also exist linear codes attaining the maximum possible cardinality $27$.

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