New quantum codes constructed from some self-dual additive $\mathbb{F}_4$-codes

TL;DR

This paper presents new quantum codes with improved minimum weights, constructed from self-dual additive $ ext{F}_4$-codes using pairs of circulant matrices, enhancing known bounds for specific parameters.

Contribution

The authors introduce a novel construction method for quantum codes using self-dual additive $ ext{F}_4$-codes based on pairs of circulant matrices, improving existing bounds.

Findings

Constructed quantum $[[n,0,d]]$ codes for specific parameters.

Achieved better lower bounds on minimum weights.

Demonstrated effectiveness of circulant matrix-based constructions.

Abstract

For $(n,d)= (66,17),(78,19)$ and $(94,21)$, we construct quantum $[[n,0,d]]$ codes which improve the previously known lower bounds on the largest minimum weights among quantum codes with these parameters. These codes are constructed from self-dual additive $\mathbb{F}_4$-codes based on pairs of circulant matrices.