Bulletin of the
Korean Mathematical Society BKMS

In this paper we will study cyclic codes over some special rings: $\mathbb{F}_{q}[u]/(u^{i})$, $\mathbb{F}_{q}[u_{1},\ldots,u_{i}]/(u_{1}^{2},u_{2}^{2},\ldots,u_{i}^{2},u_{1}u_{2}-u_{2}u_{1},\ldots,u_{k}u_{j}-u_{j}u_{k},\ldots)$, and $\mathbb{F}_{q}[u,v]/\left( u^{i},v^{j},uv-vu\right) $, where $\mathbb{F}_{q}$ is a field with $q$ elements $q=p^{r}$ for some prime number $p$ and $r\in\mathbb{N}-\{0\}$.

Keywords: cyclic codes, codes over rings, Hamming distance

MSC numbers: 94B15, 94B05