<p style='text-indent:20px;'>For any odd prime <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>, we study constacyclic codes of length id="M3">\begin{document}$ n $\end{document}</tex-math></inline-formula> over the finite commutative non-chain ring id="M4">\begin{document}$ R_{k,m} = \mathbb{F}_{p^...

Many kinds of codes which possess two cycle structures over special finite commutative chain rings, such as ${\mathbb {Z}}_{2}{\mathbb {Z}}_{4}$ -additive cyclic and quasi-cyclic fractional index etc., were proved asymptotically good....

<p style='text-indent:20px;'>This paper is about a first characterization of LCD skew constacyclic codes and some constructions cyclic negacyclic over <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_{p^2} $\end{document}</tex-math></inline-formula>.</p>

Let $\mathbb{F}_p$ be a finite field and $u$ be an indeterminate. This article studies $(1-2u^k)$-constacyclic codes over the ring $\mathcal{R}=\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p+u^{3}\mathbb{F}_{p}+\cdots+u^{k}\mathbb{F}_{p}$ where $u^{k+1}=u$. We illustrate the generator polynomials and investigate the structural properties of these codes via decomposition theorem.