Galois LCD codes over mixed alphabets

Abstract

We study (Galois) linear complementary dual codes over mixed alphabets arising from finite chain rings. We give a characterization of when a given code is of this type and when it is Galois invariant. Finally, this leads to a study of the Gray image of F p F p [θ]-linear codes, where p ∈ {2; 3} and θ θ 2 = 0, that provides F p -linear complementary dual codes.