Trifferent codes with small lengths
Sascha Kurz Β· Examples and Counterexamples Β· 2024
A code πΆ β {0, 1, 2} π of length π is called trifferent if for any three distinct elements of πΆ there exists a coordinate in which they all differ.By π (π) we denote the maximum cardinality of trifferent codes with length π.The values π (5) = 10 and π (6) = 13 were recently determined (Fiore et al., 2022).Here we determine π (7) = 16, π (8) = 20, and π (9) = 27.For the latter case π = 9 there also exist linear codes attaining the maximum possible cardinality 27.