Trifferent codes with small lengths

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Kurz, Sascha:
Trifferent codes with small lengths.
Bayreuth , 2023 . - 11 S.

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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.