SRIM and SCRIM factors of xn + 1 over finite fields and their applications
Arunwan Boripan, Somphong Jitman · Discrete Mathematics Algorithms and Applications · 2020
Self-Reciprocal Irreducible Monic (SRIM) and Self-Conjugate-Reciprocal Irreducible Monic (SCRIM) factors of [Formula: see text] over finite fields have become of interest due to their rich algebraic structures and wide applications. In this paper, these notions are extended to factors of [Formula: see text] over finite fields. Characterization and enumeration of SRIM and SCRIM factors of [Formula: see text] over finite fields are established. Simplification and recessive formulas for the number of such factors are given. Finally, applications in the study of complementary negacyclic codes are discussed.