Self-reciprocal and self-conjugate-reciprocal irreducible factors of x~n - A and their applications

摘要

In this paper, we present some necessary and sufficient conditions under which an irreducible polynomial is self-reciprocal (SR) or self-conjugate-reciprocal (SCR). By these characterizations, we obtain some enumeration formulas of SR and SCR irreducible factors of x(n) - lambda, lambda is an element of F-q*, over F-q, which are just open questions posed by Boripan et al. (2019). We also count the numbers of Euclidean and Hermitian LCD constacyclic codes and show some well-known results on Euclidean and Hermitian self-dual constacyclic codes in a simple and direct way. (C) 2020 Elsevier Inc. All rights reserved.