Repeated-root constacyclic codes of length 3ℓ^mp^s

Abstract

© 2020 AIMS. Let p be a prime different from 3, and ℓ be an odd prime different from 3 and p. In terms of generator polynomials, structures of constacyclic codes and their duals of length 3ℓmps over Fq are established, where q is a power of p. We discuss the enumeration of all cyclic codes of length 3 · 2sℓm, that generalizes the construction of [15] (2016), which is the special case of m = 1. In addition, as an application, the characterization and enumeration of all linear complementary dual cyclic codes of length 6ℓmps over Fq are obtained.