On Quantum Codes Obtained From Cyclic Codes Over ${\mathbb{F}}_2+u{\mathbb{F}}_2+u^2{\mathbb{F}}_2$

Abstract

Let $R={\mathbb{F}}_2+u{\mathbb{F}}_2+u^2{\mathbb{F}}_2$ be a non-chain finite commutative ring, where $u^3=u$. In this paper, we mainly study the construction of quantum codes from cyclic codes over $R$. We obtained self-orthogonal codes over ${\mathbb{F}}_2$ as gray images of linear and cyclic codes over $R$. The parameters of quantum codes which are obtained from cyclic code over $R$ are discussed.

9 pages. arXiv admin note: text overlap with arXiv:1407.1232 by other authors

References in corpus (1)

• On cyclic DNA codes over the Ring ${\mathbb{Z}}_4+u{\mathbb{Z}}_4$