arXiv subjects

Joël Kabore

Publications and source records attributed to Joël Kabore.

4 recordsLinked to original sources

arXiv2025

Construction of DNA codes using $θ$-skew cyclic codes over $\mathbb{F}_4 + v \mathbb{F}_4$

In this paper, we investigate $θ$-skew cyclic codes over the ring $R= \mathbb{F}_4 + v \mathbb{F}_4$, where $v^2=v$ and $θ$ is a non-trivial automorphism over $\mathbb{F}_4 + v \mathbb{F}_4$. This allows us to describe DNA code over this ring by characterizing $θ$-skew cyclic reversible DNA codes and $θ$-skew cyclic reversible complement DNA codes. We also explore the Gray images of $θ$-skew cyclic codes.

cs.IT↗

arXiv2022

Galois LCD codes over mixed alphabets

We study (Galois) linear complementary dual codes over mixed alphabets arising from finite chain rings. We give a characterization of when a given code is of We study (Galois) linear complementary dual codes over mixed alphabets arising from finite chain rings. We give a characterization of when a given code is of this type and when it is Galois invariant. Finally, this leads to a study of the Gray image of $\mathbb{F}_p\mathbb{F}_p[θ]$-linear codes, where $p\in\{2; 3\}$ and $θ\neqθ^2=0$, that provides $\mathbb{F}_p$-linear complementary dual codes.

cs.IT↗

arXiv2019

Primitive Idempotents and Constacyclic Codes over Finite Chain Rings

Let $R$ be a commutative local finite ring. In this paper, we construct the complete set of pairwise orthogonal primitive idempotents of $R[X]/ $ where $g$ is a regular polynomial in $R[X]$. We use this set to decompose the ring $R[X]/ $ and to give the structure of constacyclic codes over finite chain rings. This allows us to describe generators of the dual code $\mathcal{C}^\bot$ of a constacyclic code $\mathcal{C}$ and to characterize non-trivial self-dual constacyclic codes over finite chain rings.

cs.IT↗

arXiv2019

Skew-constacyclic codes over $\frac{\mathbb{F}_q[v]}{\langle\,v^q-v\,\rangle}$

In this paper, the investigation on the algebraic structure of the ring $\frac{\mathbb{F}_q[v]}{\langle\,v^q-v\,\rangle}$ and the description of its automorphism group, enable to study the algebraic structure of codes and their dual over this ring. We explore the algebraic structure of skew-constacyclic codes, by using a linear Gray map and we determine their generator polynomials. Necessary and sufficient conditions for the existence of self-dual skew cyclic and self-dual skew negacyclic codes over $\frac{\mathbb{F}_q[v]}{\langle\,v^q-v\,\rangle}$ are given.

cs.IT↗