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

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

Cyclic codes over the ring $F_{p} [u, v] / ⟨ u^{k}, v^{2}, u v - v u ⟩$

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Cyclic codes over the ring $F_{p} [u, v] / ⟨ u^{k}, v^{2}, u v - v u ⟩$

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Cyclic codes over the ring Fp[u,v]/⟨uk,v2,uv−vu⟩Fp​[u,v]/⟨uk,v2,uv−vu⟩

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Cyclic codes over the ring Fp[u,v]/⟨uk,v2,uv−vu⟩Fp​[u,v]/⟨uk,v2,uv−vu⟩

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Cyclic codes over the ring $F_{p} [u, v] / ⟨ u^{k}, v^{2}, u v - v u ⟩$

讲解博客

AI智能校验

Cyclic codes over the ring $F_{p} [u, v] / ⟨ u^{k}, v^{2}, u v - v u ⟩$

讲解博客

AI智能校验