New Binary Quantum Codes Derived From One-Generator Quasi-Cyclic Codes

Jingjie Lv,Junli Wang,Ruihu Li

doi:10.1109/access.2019.2923800

Abstract

In this paper, we consider a family of one-generator quasi-cyclic (QC) codes and their applications in quantum codes construction. We give a sufficient condition for one-generator QC codes to be self-orthogonal with respect to the symplectic inner product. As the computational results, five new binary quantum codes with parameters [[45,29,5]], [[63,36,7]], [[73,55,5]], [[105,71,7]], and [[105,72,7]] improving the best-known lower bounds on minimum distance in Grassl’s code tables are constructed.

Highlights

Reliable quantum information processing requires mechanisms to reduce the effects of environmental and operational noise
Similar to classical error-correcting codes, every quantum code over a finite field Fq has three basic parameters: the length (n), the dimension (k) and the minimum distance (d) that determine the performance of the quantum code
A linear code C over a finite field Fq is called cyclic if it is closed under the cyclic shift operator τ, i.e., for any codeword (c0, c1, . . . , cn−1) ∈ C, τ (c0, c1, . . . , cn−1) =

Summary

INTRODUCTION

Reliable quantum information processing requires mechanisms to reduce the effects of environmental and operational noise (decoherence). In 1998, Calderbank et al [4] proposed a method to construct binary quantum codes utilizing self-orthogonal classical error-correcting codes over finite field F4. Similar to classical error-correcting codes, every quantum code over a finite field Fq has three basic parameters: the length (n), the dimension (k) and the minimum distance (d) that determine the performance of the quantum code. In 2018, Galindo et al [9] used two-generates QC codes of short length which are dualcontaining to construct quantum codes, and they have gained some quantum codes with good parameters. Inspired by the previous work, we will originally consider quantum codes construction from self-orthogonal one-generator QC codes with respect to symplectic inner product.

PRELIMINARIES

CONSTRUCTION OF QUANTUM CODES

SOME NEW BINARY QUANTUM CODES

CONCLUSION