New self-dual additive $\mathbb{F}_4$-codes constructed from circulant graphs

TL;DR

This paper introduces new self-dual additive -codes derived from circulant graphs to construct quantum codes with previously unattainable parameters, advancing quantum error correction capabilities.

Contribution

It presents the first construction of quantum codes with specific parameters using self-dual additive -codes from circulant graphs.

Findings

Constructed quantum -codes for (n,d)=(56,15), (57,15), (58,16), (63,16), (67,17), (70,18), (71,18), (79,19), (83,20), (87,20), (89,21), (95,20).

First-time realization of these quantum code parameters.

Demonstrated the effectiveness of circulant graph-based -codes in quantum code construction.

Abstract

In order to construct quantum $[[n,0,d]]$ codes for $(n,d)=(56,15)$, $(57,15)$, $(58,16)$, $(63,16)$, $(67,17)$, $(70,18)$, $(71,18)$, $(79,19)$, $(83,20)$, $(87,20)$, $(89,21)$, $(95,20)$, we construct self-dual additive $\mathbb{F}_4$-codes of length $n$ and minimum weight $d$ from circulant graphs. The quantum codes with these parameters are constructed for the first time.