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The maximum cardinality of trifferent codes with lengths 5 and 6 (2201.06846v1)
Published 18 Jan 2022 in math.CO, cs.IT, and math.IT
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 $\mathcal{T}(6) = 13$.