New Binary Quantum Codes Constructed from Quasi-Cyclic Codes

TL;DR

This paper introduces a new method for constructing binary quantum codes from quasi-cyclic codes, resulting in 44 codes that surpass existing bounds in minimum distance and performance.

Contribution

It presents a novel construction approach using symplectic dual-containing quasi-cyclic codes and provides explicit new quantum codes with improved parameters.

Findings

Constructed 8 quantum codes exceeding known results.

Generated 36 additional codes improving minimum distance bounds.

Established sufficient conditions for symplectic dual-containing properties.

Abstract

It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be symplectic dual-containing. Then, a new method for constructing binary quantum codes using symplectic dual-containing codes is proposed. As an application, we construct 8 binary quantum codes that exceed the best-known results. Further, another 36 new binary quantum codes are obtained by propagation rules, all of which improve the lower bound on the minimum distances.