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

Abstract

In this paper, we investigate cyclic codes over the ring ${\mathbb{F}}_p[u,v,w]⟨u^2,$ $v^2,w^2$, $uv-vu,vw-wv,uw-wu⟩$, where $p$ is a prime number. Which is a part of family of Frobenius rings. We find a unique set of generators for these codes and characterize the free cyclic codes. We also study the rank and the Hamming distance of these codes. We also constructs some good $p-ary$ codes as the Gray images of these cyclic codes.

arXiv commentRewriting of Section 4. arXiv admin note: substantial text overlap with arXiv:1508.07034, arXiv:1405.5981