Hermitian hull of some GRS codes and new EAQMDS codes
Oisin Campion, Rodrigo San-Jos\'e
TL;DR
This paper investigates the Hermitian hull of GRS codes to determine the entanglement needed for quantum error correction, providing explicit formulas and new quantum code parameters.
Contribution
It introduces a method to compute the Hermitian hull dimension of GRS codes and constructs new EAQMDS codes with flexible parameters.
Findings
Explicit formulas for hull dimensions of GRS codes
New EAQMDS codes with diverse parameters
Reduced entanglement requirements for quantum codes
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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Taxonomy
TopicsCoding theory and cryptography · Satellite Communication Systems