# Good Stabilizer Codes from Quasi-Cyclic Codes over $\mathbb{F}_4$ and $\mathbb{F}_9$

## TL;DR

This paper develops new quantum stabilizer codes from quasi-cyclic codes over finite fields, achieving improved parameters and filling gaps in existing literature for qubit and qutrit systems.

## Contribution

It introduces a systematic construction of quantum codes using quasi-cyclic codes with large Hermitian hulls, leading to better or best-known quantum code parameters.

## Key findings

- Several quantum codes with improved parameters over existing records.
- Quantum codes with best-known performance in multiple instances.
- Systematic construction method for qutrit stabilizer codes.

## Abstract

We apply quantum Construction X on quasi-cyclic codes with large Hermitian hulls over $\mathbb{F}_4$ and $\mathbb{F}_9$ to derive good qubit and qutrit stabilizer codes, respectively. In several occasions we obtain quantum codes with stricly improved parameters than the current record. In numerous other occasions we obtain quantum codes with best-known performance. For the qutrit ones we supply a systematic construction to fill some gaps in the literature.