Quantum LDPC Codes Based on Cocyclic Block Matrices

Author:

Li Yuan1,Guo Ying2ORCID

Affiliation:

1. School of Electronic Information Engineering, Shanghai Dianji University, Shanghai 200240, China

2. School of Computer Science and Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China

Abstract

Motivated by a family of binary cocyclic block matrices over GF(2), we proposed a construction method to gain the stabilizer of long-length quantum error-correction codes (QECCs). Stabilizer quantum codes (SQCs) can be obtained by the different rows of the yielded circulant permutation matrices; hence, the quantum codes have the virtue of a fast construction algorithm. The recursive relation of a block matrix is employed in the proposed approach, so that the generator matrix of quantum cocyclic codes with long length can be constructed easily. Furthermore, the obtained quantum codes have the low-density advantage of there being no 4-cycles in the Tanner graph.

Funder

Natural Science Foundation of Shanghai

Publisher

MDPI AG

Subject

General Physics and Astronomy

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