# Quantum codes derived from cyclic codes

## TL;DR

This paper introduces a method to construct new nonbinary quantum codes with favorable parameters using cyclic codes and the CSS construction, highlighting the existence of specific classical cyclic codes with particular defining sets.

## Contribution

It presents a novel construction of quantum codes from cyclic codes with defining sets containing consecutive integers, expanding the toolkit for quantum error correction.

## Key findings

- Successfully constructed new quantum codes with good parameters.
- Proved the existence of cyclic codes with defining sets of a single cyclotomic coset containing consecutive integers.
- Demonstrated the applicability of the CSS construction to these cyclic codes.

## Abstract

In this note, we present a construction of new nonbinary quantum codes with good parameters. These codes are obtained by applying the Calderbank-Shor-Steane (CSS) construction. In order to do this, we show the existence of (classical) cyclic codes whose defining set consists of only one cyclotomic coset containing at least two consecutive integers.