Self-reciprocal and self-conjugate-reciprocal irreducible factors of $x^n-\lambda$ and their applications

Yansheng Wu; Qin Yue; Shuqin Fan

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arXiv · 2001.04766

Self-reciprocal and self-conjugate-reciprocal irreducible factors of $x^n-\lambda$ and their applications

Yansheng Wu·Qin Yue·Shuqin Fan

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Abstract

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 $x^n-\lambda$, $\lambda\in \Bbb F_q^*$, over $\Bbb F_q$, which are just open questions posed by Boripan {\em 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.

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Yansheng Wu, Qin Yue, Shuqin Fan. 2020-01-14. Self-reciprocal and self-conjugate-reciprocal irreducible factors of $x^n-\lambda$ and their applications. https://arxiv.org/abs/2001.04766

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