Two New Zero-Dimensional Qubit Codes from Bordered Metacirculant Construction

TL;DR

This paper introduces two new zero-dimensional qubit stabilizer codes with high minimum distances, constructed via symplectic self-dual additive codes over 4 using modified adjacency matrices of metacirculant graphs.

Contribution

The paper presents the first construction of specific qubit stabilizer codes with parameters [[81,0,20]] and [[94,0,22]] using a novel graph-based method.

Findings

Successfully constructed new qubit codes with high minimum distances.

Demonstrated the effectiveness of metacirculant graph modifications in code design.

Provided a randomized search procedure for finding suitable graphs.

Abstract

We construct qubit stabilizer codes with parameters $[[81, 0, 20]]$ and $[[94, 0, 22]]$ for the first time. We use symplectic self-dual additive codes over $\mathbb{F}_4$ built by modifying the adjacency matrices of suitable metacirculant graphs found by a randomized search procedure.