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

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