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

Sukhamoy Pattanayak; Abhay Kumar Singh; Pratyush Kumar

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

Information Theory 2016-01-13 v2 math.IT

Authors: Sukhamoy Pattanayak , Abhay Kumar Singh , Pratyush Kumar

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.

Keywords

quantum error-correcting code coding theory

Cite

@article{arxiv.1601.02328,
  title  = {On Quantum Codes Obtained From Cyclic Codes Over $\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$},
  author = {Sukhamoy Pattanayak and Abhay Kumar Singh and Pratyush Kumar},
  journal= {arXiv preprint arXiv:1601.02328},
  year   = {2016}
}

Comments

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

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