Self-reciprocal and self-conjugate-reciprocal irreducible factors of $x^n-\lambda$ and their applications
| Autor: | Wu, Yansheng, Yue, Qin, Fan, Shuqin |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 14 pages. To appear in Finite Fields and Their Applications |
| Databáze: | arXiv |
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