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arXiv · 1902.10477

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

Joël Kabore·Alexandre Fotue-Tabue·Kenza Guenda·Mohammed E. Charkani
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Abstract

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.

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Joël Kabore, Alexandre Fotue-Tabue, Kenza Guenda, Mohammed E. Charkani. 2019-02-27. Skew-constacyclic codes over $\frac{\mathbb{F}_q[v]}{\langle\,v^q-v\,\rangle}$. https://arxiv.org/abs/1902.10477

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