Patrick Solé

Skew Cyclic Codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$

2015 · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

In this article, we study skew cyclic codes over $R=\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$, where $q=p^{m}$, $p$ is an odd prime and v3=v. We describe the generator polynomials of skew cyclic codes over this ring and investigate the structural …

Three-weight codes and the quintic construction

2016 · arXiv (Cornell University)

We construct a class of three-Lee-weight and two infinite families of five-Lee-weight codes over the ring $R=\mathbb{F}_2 +v\mathbb{F}_2 +v^2\mathbb{F}_2 +v^3\mathbb{F}_2 +v^4\mathbb{F}_2,$ where $v^5=1.$ The same ring occurs in the quintic construction of binary quasi-cyclic codes. …

On self-dual four circulant codes

2017 · arXiv (Cornell University)

Four circulant codes form a special class of $2$-generator, index $4$, quasi-cyclic codes. Under some conditions on their generator matrices they can be shown to be self-dual. Artin primitive root conjecture shows the existence of …

On self-dual double circulant codes

2016 · arXiv (Cornell University)

Self-dual double circulant codes of odd dimension are shown to be dihedral in even characteristic and consta-dihedral in odd characteristic. Exact counting formulae are derived for them and used to show they contain families of …