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Quantum Codes Derived from One-Generator Quasi-Cyclic Codes with Hermitian Inner Product

  • Jingjie Lv
  • Ruihu LiEmail author
  • Junli Wang
Article

Abstract

In this paper, we consider a family of one-generator quasi-cyclic codes and their applications in quantum codes construction. We give a sufficient condition for self-orthogonality with respect to Hermitian inner product. By virtue of the well-known MacWilliams equations, some binary and ternary stabilizer quantum codes with good parameters are constructed. Furthermore, we present a lower bound on the Hermitian dual distance of these involved codes. As the computational results, some good stabilizer quantum codes over small finite fields are obtained.

Keywords

Quantum codes Quasi-cyclic codes Hermitian inner product 

Notes

Acknowledgments

This work is supported by National Natural Science Foundation of China (Nos.11471011, 11801564) and Natural Science Foundation of Shaanxi (No.2017JQ1032).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Basic SciencesAir Force Engineering UniversityXi’anPeople’s Republic of China

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