Extended quasi-cyclic constructions of quantum codes and entanglement-assisted quantum codes
Abstract
Construction of quantum codes and entanglement-assisted quantum codes with good parameters via classical codes is an important task for quantum computing and quantum information. In this paper, by a family of one-generator quasi-cyclic codes, we provide quasi-cyclic extended constructions that preserve the self-orthogonality to obtain stabilizer quantum codes. As for the computational results, some binary and ternary stabilizer codes with good parameters are constructed. Moreover, we present methods to construct maximal-entanglement entanglement-assisted quantum codes by means of the class of quasi-cyclic codes and their extended codes. As an application, some good maximal-entanglement entanglement-assisted quantum codes are obtained and their parameters are compared.
Cite
@article{arxiv.2009.02543,
title = {Extended quasi-cyclic constructions of quantum codes and entanglement-assisted quantum codes},
author = {Jingjie Lv and Ruihu Li and Yu Yao},
journal= {arXiv preprint arXiv:2009.02543},
year = {2020}
}