# Quantum Codes from Linear Codes over Finite Chain Rings

## TL;DR

This paper introduces two novel methods for constructing quantum codes using linear codes over finite chain rings, enhancing quantum error correction techniques with new code parameters and constructions.

## Contribution

It presents two new constructions of quantum codes from linear codes over finite chain rings, expanding the toolkit for quantum error correction.

## Key findings

- Good parameters of quantum codes from cyclic codes over finite chain rings.
- Construction methods based on CSS applied to self-dual codes and Gray images.
- Enhanced quantum code parameters demonstrated.

## Abstract

In this paper, we provide two methods of constructing quantum codes from linear codes over finite chain rings. The first one is derived from the Calderbank-Shor-Steane (CSS) construction applied to self-dual codes over finite chain rings. The second construction is derived from the CSS construction applied to Gray images of the linear codes over finite chain ring $\mathbb{F}_{p^{2m}}+u\mathbb{F}_{p^{2m}}$. The good parameters of quantum codes from cyclic codes over finite chain rings are obtained.