Hermitian hull of some GRS codes and new EAQMDS codes
Information Theory
2025-07-25 v1 math.IT
Abstract
We study the Hermitian hull of a particular family of generalized Reed-Solomon codes. The problem of computing the dimension of the hull is translated to a counting problem in a lattice. By solving this problem, we provide explicit formulas for the dimension of the hull, which determines the minimum number required of maximally entangled pairs for the associated entanglement-assisted quantum error-correcting codes. This flexible construction allows to obtain a wide range of entanglement-assisted quantum MDS codes, as well as new parameters.
Keywords
Cite
@article{arxiv.2507.18361,
title = {Hermitian hull of some GRS codes and new EAQMDS codes},
author = {Oisin Campion and Rodrigo San-José},
journal= {arXiv preprint arXiv:2507.18361},
year = {2025}
}