Trifferent codes with small lengths

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 $T\left(n\right)$ we denote the maximum cardinality of trifferent codes with length $n$. The values $T\left(5\right)=10$ and $T\left(6\right)=13$ were recently determined (Fiore et al., 2022). Here we determine $T\left(7\right)=16$, $T\left(8\right)=20$, and $T\left(9\right)=27$. For the latter case $n=9$ there also exist linear codes attaining the maximum possible cardinality 27.