Trifferent codes with small lengths

Titelangaben

Kurz, Sascha:
Trifferent codes with small lengths.
In: Examples and Counterexamples. Bd. 5 (2024) . - 100139.
ISSN 2666-657X
DOI: https://doi.org/10.1016/j.exco.2024.100139

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Abstract

A code C over the alphabet {0,1,2} with length n is called trifferent if for any three distinct elements of C there exists a coordinate in which they all differ. By T(n) we denote the maximum cardinality of trifferent codes with length n. T(5)=10 and T(6)=13 were recently determined. Here we determine T(7)=16, T(8)=20, and T(9)=27. For the latter case n=9 there also exist linear codes attaining the maximum possible cardinality 27.