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Trifferent codes with small lengths (2310.13563v1)
Published 20 Oct 2023 in math.CO and cs.DM
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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