Self-Reciprocal Polynomials and Coterm Polynomials

We classify all self-reciprocal polynomials arising from reversed Dickson polynomials over $\mathbb{Z}$ and $\mathbb{F}_p$, where $p$ is prime. As a consequence, we also obtain coterm polynomials arising from reversed Dickson polynomials.Comment: 21 page

Reversible Codes and Its Application to Reversible DNA Codes over F4kF_{4^k}

Coterm polynomials are introduced by Oztas et al. [a novel approach for constructing reversible codes and applications to DNA codes over the ring $F_2[u]/(u^{2k}-1)$, Finite Fields and Their Applications 46 (2017).pp. 217-234.], which generate reversible codes. In this paper, we generalize the coterm polynomials and construct some reversible codes which are optimal codes by using $m$-quasi-reciprocal polynomials. Moreover, we give a map from DNA $k$-bases to the elements of $F_{4^k}$, and construct reversible DNA codes over $F_{4^k}$ by DNA-$m$-quasi-reciprocal polynomials

Self-reciprocal and self-conjugate-reciprocal irreducible factors of xn−λx^n-\lambda and their applications

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 Application