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

preprint2015arXivOpen access

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

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

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Cyclic codes over the ring Fp[u,v]/⟨uk,v2,uv−vu⟩\mathbb{F}_p[u,v] / \langle u^k,v^2,uv-vu\rangleFp​[u,v]/⟨uk,v2,uv−vu⟩

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