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Classical Goppa codes are a well-known class of codes with applications in code-based cryptography, which are a special case of alternant codes. Many papers are devoted to the search for Goppa codes with a cyclic extension or with a cyclic…
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…
A ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive code ${\cal C}\subseteq{\mathbb{Z}}_2^\alpha\times{\mathbb{Z}}_4^\beta$ is called cyclic if the set of coordinates can be partitioned into two subsets, the set of ${\mathbb{Z}}_2$ and the set of…
We construct codes over the ring $\mathbb{F}_2+u\mathbb{F}_2$ with $u^2=0$. These code are designed for use in DNA computing applications. The codes obtained satisfy the reverse complement constraint, the $GC$ content constraint and avoid…
In an interesting paper Professor Cunsheng Ding provided three constructions of cyclic codes of length being a product of two primes. Numerical data shows that many codes from these constructions are best cyclic codes of the same length and…
We propose a unified method to construct multicyclic codes of arbitrary dimension $r$ over $\mathbb{F}_q$. The approach relies on $r$-dimensional primitive idempotents defined as tensor products of univariate ones, combined with…
Let $\mathbb{F}_q$ be a finite field of $q=p^m$ elements where $p$ is a prime and $m$ is a positive integer. This paper considers $(\gamma,\Delta)$-cyclic codes over a class of finite non-chain commutative rings…
Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this…
Let $f(u)$ be a polynomial of degree $m, m \geq 2,$ which splits into distinct linear factors over a finite field $\mathbb{F}_{q}$. Let $\mathcal{R}=\mathbb{F}_{q}[u]/\langle f(u)\rangle$ be a finite non-chain ring. In an earlier paper, we…
In this work, we study a class of skew cyclic codes over the ring $R:=\mathbb{Z}_4+v\mathbb{Z}_4,$ where $v^2=v,$ with an automorphism $\theta$ and a derivation $\Delta_\theta,$ namely codes as modules over a skew polynomial ring…
In this paper we investigate repeated root cyclic and negacyclic codes of length $p^rm$ over $\mathbb{F}_{p^s}$ with $(m,p)=1$. In the case $p$ odd, we give necessary and sufficient conditions on the existence of negacyclic self-dual codes.…
The hulls of linear and cyclic codes over finite fields have been of interest and extensively studied due to their wide applications. In this paper, the hulls of cyclic codes of length $n$ over the ring $\mathbb{Z}_4$ have been focused on.…
Construction of subspace codes with good parameters is one of the most important problems in random network coding. In this paper we present first a generalization of the concept of cyclic subspaces codes and further we show that the usual…
In this paper, we study skew cyclic codes over the ring $R=\F_q+u\F_q+v\F_q+uv\F_q$, where $u^{2}=u,v^{2}=v,uv=vu$, $q=p^{m}$ and $p$ is an odd prime. We investigate the structural properties of skew cyclic codes over $R$ through a…
Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a polynomial ring. The structure of the ambient ring of polycyclic…
In this article, we study the algebraic structure of double cyclic codes of length $(m, n)$ over $\mathbb{F}_4$ and we give a necessary and sufficient condition for a double cyclic code over $\mathbb{F}_4$ to be reversible. Also, we…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Perfect nonlinear monomials were employed to…
Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first…
For any positive integers $m$ and $k$, existing literature only determines the number of all Euclidean self-dual cyclic codes of length $2^k$ over the Galois ring ${\rm GR}(4,m)$, such as in [Des. Codes Cryptogr. (2012) 63:105--112]. Using…
The ring in the title is the first non commutative ring to have been used as alphabet for block codes. The original motivation was the construction of some quaternionic modular lattices from codes. The new application is the construction of…