The maximum cardinality of trifferent codes with lengths 5 and 6

Abstract

A code $C\subseteq {\{0,1,2\}}^n$ is said to be trifferent with length $n$ when for any three distinct elements of $C$ there exists a coordinate in which they all differ. Defining $T\left(n\right)$ as the maximum cardinality of trifferent codes with length $n$, $T\left(n\right)$ is unknown for $n\ge 5$. In this note, we use an optimized search algorithm to show that $T\left(5\right)=10$ and $T\left(6\right)=13$.