Self-conjugate-reciprocal irreducible monic factors of x~n - 1 over finite fields and their applications

摘要

Self-reciprocal and self-conjugate-reciprocal polynomials over finite fields have been of interest due to their rich algebraic structures and wide applications. Self-reciprocal irreducible monic factors of x(n) - 1 over finite fields and their applications have been quite well studied. In this paper, self-conjugate reciprocal irreducible monic (SCRIM) factors of x(n) - 1 over finite fields of square order are focused on. The characterization of such factors is given together with the enumeration formula. In many cases, recursive formulas for the number of SCRIM factors of x(n) - 1 are given as well. As applications, Hermitian complementary dual cyclic codes over finite fields and Hermitian self-dual cyclic codes over finite chain rings of prime characteristic are discussed. (C) 2018 Elsevier Inc. All rights reserved.