Related papers: Repeated-root constacyclic codes over finite commu…

Let $\mathcal{R}=\mathbb{F}_{p^m}[u]/\langle u^3 \rangle $ be the finite commutative chain ring with unity, where $p$ is a prime, $m$ is a positive integer and $\mathbb{F}_{p^m}$ is the finite field with $p^m$ elements. In this paper, we…

In this paper we investigate the structure of repeated root constacyclic codes of length $2^amp^r$ over $\mathbb{F}_{p^s}$ with $a\geq1$ and $(m,p)=1$. We characterize the codes in terms of their generator polynomials. This provides simple…

For $\lambda$ an $n$-th power of a unit in a finite chain ring we prove that $\lambda$-constacyclic repeated-root codes over some finite chain rings are equivalent to cyclic codes. This allows us to simplify the structure of some…

Let $p$ be an odd prime, and let $m$ be a positive integer satisfying $p^m \equiv 3~(\text{mod }4).$ Let $\mathbb{F}_{p^m}$ be the finite field with $p^m$ elements, and let $R=\mathbb{F}_{p^m}[u]/\left<u^2\right>$ be the finite commutative…

For any different odd primes $\ell$ and $p$, structure of constacyclic codes of length $2\ell^mp^n$ over a finite field $\mathbb F_q$ of characteritic $p$ and their duals is established in term of their generator polynomials. Among other…

In this paper, we study some repeated-root two-dimensional cyclic and constacyclic codes over a finite field $F=\mathbb{F}_q$. We obtain the generator matrices and generator polynomials of these codes and their duals. We also investigate…

Let $p\neq3$ be any prime and $l\neq3$ be any odd prime with $gcd(p,l)=1$. $F_{q}^{*}=\langle\xi\rangle$ is decomposed into mutually disjoint union of $gcd(q-1,3lp^{s})$ coset over the subgroup $\langle\xi^{3lp^{s}}\rangle$, where $\xi$ is…

Many kinds of codes which possess two cycle structures over two special finite commutative chain rings, such as ${\Bbb Z}_2{\Bbb Z}_4$-additive cyclic codes and quasi-cyclic codes of fractional index etc., were proved asymptotically good.…

We study constacyclic codes, of length $np^s$ and $2np^s$, that are generated by the polynomials $(x^n + \gamma)^{\ell}$ and $(x^n - \xi)^i(x^n + \xi)^j$\ respectively, where $x^n + \gamma$, $x^n - \xi$ and $x^n + \xi$ are irreducible over…

This study aims to determine the algebraic structures of $\alpha$-constacyclic codes of length $3p^s$ over the finite commutative non-chain ring $\mathcal{R}=\frac{\mathbb{F}_{p^m}[u, v]}{\langle u^2, v^2, uv-vu\rangle}$, for a prime $p…

Let $\mathbb{F}_{p^m}$ be a finite field of cardinality $p^m$ where $p$ is an odd prime, $n$ be a positive integer satisfying ${\rm gcd}(n,p)=1$, and denote $R=\mathbb{F}_{p^m}[u]/\langle u^e\rangle$ where $e\geq 4$ be an even integer. Let…

Due to the wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an interesting research topic in coding theory. In this paper, let $p$ be a prime with $p\ge 7$. We determine the…

We give the structure of $\lambda$-constacyclic codes of length $p^sm$ over $R=\mathbb{F}_{p^r}+u \mathbb{F}_{p^r}+...+ u^{e-1}\mathbb{F}_{p^r}$ with $\lambda \in \F_{p^r}^*$. We also give the structure of $\lambda$-constacyclic codes of…

Let $R$ be a commutative local finite ring. In this paper, we construct the complete set of pairwise orthogonal primitive idempotents of $R[X]/<g>$ where $g$ is a regular polynomial in $R[X]$. We use this set to decompose the ring…

In this paper, necessary and sufficient conditions for the reversibility of a cyclic code of arbitrary length over a finite commutative chain ring have been derived. MDS reversible cyclic codes having length p^s over a finite chain ring…

In this paper, several families of irreducible constacyclic codes over finite fields and their duals are studied. The weight distributions of these irreducible constacyclic codes and the parameters of their duals are settled. Several…

In this paper, we determine depth spectra of all repeated-root $(\alpha+\gamma \beta)$-constacyclic codes of arbitrary lengths over a finite commutative chain ring $\mathcal{R},$ where $\alpha$ is a non-zero element of the Teichm\"{u}ller…

Let $p$ be an odd prime. In this paper, we have determined the Hamming distances for constacyclic codes of length $2p^s$ over the finite commutative non-chain ring $\mathcal{R}=\frac{\mathbb{F}_{p^m}[u, v]}{\langle u^2, v^2, uv-vu\rangle}$.…

Constacyclic codes over finite fields are an important class of linear codes as they contain distance-optimal codes and linear codes with best known parameters. They are interesting in theory and practice, as they have the constacyclic…

Determining the weight distribution of a linear code is a classical and fundamental topic in coding theory that has been extensively investigated. Repeated-root cyclic codes, which form a significant subclass of error-correcting codes, have…