Improved Quantum Codes from Metacirculant Graphs via Self-Dual Additive $\mathbb{F}_4$-Codes

TL;DR

This paper introduces new quantum error-correcting codes derived from metacirculant graphs and self-dual additive codes over , achieving improved parameters and performance over previous codes.

Contribution

It presents the first construction of certain -based quantum codes from metacirculant graphs, with enhanced parameters and performance.

Findings

Constructed new -based quantum codes with parameters (78,20), (90,21), (91,22), (93,21), (96,21)

Secondary methods yield codes surpassing previous best-known performance

Demonstrated the effectiveness of metacirculant graph-based codes in quantum error correction

Abstract

We use symplectic self-dual additive codes over $\mathbb{F}_4$ obtained from metacirculant graphs to construct, for the first time, $[[\ell, 0, d ]]$ qubit codes with parameters $(\ell,d) \in \{(78, 20), (90, 21), (91, 22), (93,21),(96,21)\}$. Secondary constructions applied to the qubit codes result in many qubit codes that perform better than the previous best-known.