# Some optimal entanglement-assisted quantum codes constructed from quaternary Hermitian linear complementary dual codes

## TL;DR

This paper constructs new optimal entanglement-assisted quantum codes from quaternary Hermitian linear complementary dual codes, demonstrating their existence for specific parameters and analyzing their minimum weights.

## Contribution

The paper introduces a method to construct optimal entanglement-assisted quantum codes from quaternary Hermitian LCD codes for specific parameters.

## Key findings

- Existence of optimal codes for given parameters.
- Codes constructed from Hermitian LCD codes.
- Observations on maximum minimum weights.

## Abstract

We establish the existence of optimal maximal entanglement entanglement-assisted quantum $[[n,k,d;n-k]]_2$ codes for $(n,k,d)=(14,6,7)$, $(15,7,7)$, $(17,6,9)$, $(17,7,8)$, $(19,7,9)$ and $(20,7,10)$. These codes are obtained from quaternary Hermitian linear complementary dual codes. We also give some observation on the largest minimum weights.