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In this paper, we study an special type of cyclic codes called skew cyclic codes over the ring $\mathbb{F}_p+v\mathbb{F}_p+v^2\mathbb{F}_p$, where $p$ is a prime number. This set of codes are the result of module (or ring) structure of the skew polynomial ring $(\mathbb{F}_p+v\mathbb{F}_p+v^2\mathbb{F}_p)[x;\theta]$ where $v^3=1$ and $\theta$ is an $\mathbb{F}_p$-automorphism such that $\theta(v)=v^2$. We show that when $n$ is even, these codes are either principal or generated by two elements. The generator and parity check matrix are proposed. Some examples of linear codes with optimum Hamming distance are also provided.
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참고문헌 (9)
참고문헌 신청
T. Abualrub / 2010 / On the construction of skew quasi-cyclic codes / IEEE Trans. Inform. Theory 56(5):2081~2090
T. Blackford / 2003 / Negacyclic codes over Z4 of even length / IEEE Trans. Inform. Theory 49(6):1417~1424
A. Bonnecaze / 1999 / Cyclic codes and self-dual codes over F2 + uF2 / IEEE Trans. Inform. Theory 45(4):1250~1255
D. Boucher / 2007 / Skew-cyclic codes / Appl. Algebra Engrg. Comm. Comput 18(4):379~389
D. Boucher / 2008 / Skew constacyclic codes over Galois rings / Adv. Math. Commun 2(3):273~292
T. Blackford / 2003 / Negacyclic codes over Z4 of even length / IEEE Trans. Inform. Theory 49(6):1417~1424
A. Bonnecaze / 1999 / Cyclic codes and self-dual codes over F2 + uF2 / IEEE Trans. Inform. Theory 45(4):1250~1255
D. Boucher / 2007 / Skew-cyclic codes / Appl. Algebra Engrg. Comm. Comput 18(4):379~389
D. Boucher / 2008 / Skew constacyclic codes over Galois rings / Adv. Math. Commun 2(3):273~292
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