# On Euclidean Hulls of MDS Codes

## TL;DR

This paper introduces a new method for constructing MDS codes with customizable Euclidean hull dimensions using generalized Reed-Solomon codes, expanding previous approaches in the field.

## Contribution

It presents a general construction technique for MDS codes with arbitrary Euclidean hull dimensions based on self-orthogonal GRS codes, surpassing prior methods.

## Key findings

- Constructed (extended) GRS codes with specified Euclidean hull dimensions.
- Demonstrated the generality of the new construction over previous methods.
- Provided a framework for designing MDS codes with desired hull properties.

## Abstract

In this paper, we propose a mechanism on the constructions of MDS codes with arbitrary dimensions of Euclidean hulls. Precisely, we construct (extended) generalized Reed-Solomon(GRS) codes with assigned dimensions of Euclidean hulls from self-orthogonal GRS codes. It turns out that our constructions are more general than previous works on Euclidean hulls of (extended) GRS codes.