@article{article_168454, title={Skew cyclic codes over $F_{q}+uF_{q}+vF_{q}+uvF_{q}$}, journal={Journal of Algebra Combinatorics Discrete Structures and Applications}, volume={2}, pages={163–168}, year={2015}, DOI={10.13069/jacodesmath.90080}, author={Yao, Ting and Shi, Minjia and Solé, Patrick}, keywords={Linear codes, Skew cyclic codes, Gray map, Generator polynomial}, abstract={<p>In this paper, we study skew cyclic codes over the ring $R=\mathbb{F}_{q}+u\mathbb{F}_{q}+v\mathbb{F}_{q}+uv\mathbb{F}_{q}$, 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 decomposition theorem. Furthermore, we give a formula for the number of skew cyclic codes of length $n$ over $R.$ </p>}, number={3}, publisher={iPeak Academy}