New Quantum Stabilizer Codes from generalized Monomial-Cartesian Codes constructed using two different generalized Reed-Solomon codes
Information Theory
2025-12-19 v1 math.IT
Abstract
In this work, we define Generalized Monomial Cartesian Codes (GMCC), which constitute a natural extension of generalized Reed-Solomon codes. We describe how two different generalized Reed-Solomon codes can be combined to construct one GMCC. We further establish sufficient conditions ensuring that the GMCC are Hermitian self-orthogonal, thus leading to new constructions of quantum codes.
Keywords
Cite
@article{arxiv.2512.16482,
title = {New Quantum Stabilizer Codes from generalized Monomial-Cartesian Codes constructed using two different generalized Reed-Solomon codes},
author = {Oisin Campion and Fernando Hernando and Gary McGuire},
journal= {arXiv preprint arXiv:2512.16482},
year = {2025}
}