Additive cyclic codes over Fq3

Official URL: https://dx.doi.org/10.1142/S0219498825503396

Let Fqbe an arbitrary finite field and n ≥ 2 be an integer with gcd(n, q) = 1. We study all Fq-linear additive cyclic codes over F q3of length n systematically. This is much more complicated compared to the same task over F q2. We obtain a canonical unique representation. We explicitly obtain the dual codes in the canonical form under the Euclidean and trace the Galois inner products. We characterize and construct large classes of complementary dual codes among Fq-linear additive cyclic codes over F q3of length n under the trace Euclidean and the trace Galois inner products. We obtain interesting differences depending on the canonical representation and also on the inner products. We also study subfield subcodes and trace (onto Fq) codes.