Hermitian hull of some GRS codes and new EAQMDS codes

Oisin Campion; Rodrigo San-José

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arXiv · 2507.18361

Hermitian hull of some GRS codes and new EAQMDS codes

Oisin Campion·Rodrigo San-José

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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.

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Oisin Campion, Rodrigo San-José. 2025-07-24. Hermitian hull of some GRS codes and new EAQMDS codes. https://arxiv.org/abs/2507.18361

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