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

TL;DR

This paper explores constructing quantum error-correcting codes from cyclic codes over a specific finite ring, expanding the methods for quantum code design using algebraic structures.

Contribution

It introduces a new approach to derive quantum codes from cyclic codes over a non-chain finite ring, including the construction of self-orthogonal codes over f_2.

Findings

Self-orthogonal codes over f_2 obtained from cyclic codes over R

Parameters of quantum codes derived from cyclic codes over R

Method for constructing quantum codes via Gray images

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.