The maximum cardinality of trifferent codes with lengths 5 and 6

Abstract

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

Accepted for publication at Examples and Counterexamples

References in corpus (2)

• Matrix Algebras and Semidefinite Programming Techniques for Codes
• New bounds for perfect $k$-hashing