Cyclic codes over the ring ${\mathbb{F}}_p[u,v]/⟨u^k,v^2,uv-vu⟩$

Abstract

Let $p$ be a prime number. In this paper, we discuss the structures of cyclic codes over the ring ${\mathbb{F}}_p[u,v]/⟨u^k,v^2,uv-vu⟩$. We find a unique set of generators for these codes. We also study the rank and the Hamming distance of these codes.

arXiv comment34 pages