Self-reciprocal and self-conjugate-reciprocal irreducible factors of x^n-λ and their applications

01/14/2020

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by   Yansheng Wu, et al.

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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-λ, λ∈ 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.