# Quaternary Hermitian linear complementary dual codes

## TL;DR

This paper investigates the maximum minimum weights of quaternary Hermitian linear complementary dual codes, establishing nonexistence conditions, determining these weights for dimension 3, and constructing new quantum codes from these classical codes.

## Contribution

It provides new nonexistence conditions, fully determines maximum minimum weights for dimension 3, and constructs novel quantum codes from classical quaternary Hermitian LCD codes.

## Key findings

- Maximum minimum weights for dimension 3 are fully determined.
- Nonexistence conditions for large minimum weights are established.
- New quantum codes are constructed from classical codes.

## Abstract

The largest minimum weights among quaternary Hermitian linear complementary dual codes are known for dimension $2$. In this paper, we give some conditions for the nonexistence of quaternary Hermitian linear complementary dual codes with large minimum weights. As an application, we completely determine the largest minimum weights for dimension $3$, by using a classification of some quaternary codes. In addition, for a positive integer $s$, a maximal entanglement entanglement-assisted quantum $[[21s+5,3,16s+3;21s+2]]$ codes is constructed for the first time from a quaternary Hermitian linear complementary dual $[26,3,19]$ code.