The maximum cardinality of trifferent codes with lengths 5 and 6

01/18/2022

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by   Stefano Della Fiore, et al.

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A code 𝒞⊆{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(n) as the maximum cardinality of trifferent codes with length n, 𝒯(n) is unknown for n ≥ 5. In this note, we use an optimized search algorithm to show that 𝒯(5) = 10 and 𝒯(6) = 13.