SRIM and SCRIM Factors of x^n+1 over Finite Fields and Their Applications

09/09/2019

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by   Arunwan Boripan, et al.

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Self-Reciprocal Irreducible Monic (SRIM) and Self-Conjugate-Reciprocal Irreducible Monic (SRCIM) factors of x^n-1 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 x^n+ 1 over finite fields. Characterization and enumeration of SRIM and SCRIM factors of x^n+1 over finite fields are established. Simplification and recessive formulas for the number of such factors are given. Finally, applications in the studied of complementary negacyclic codes are discussed.