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arXiv · 2512.16482

New Quantum Stabilizer Codes from generalized Monomial-Cartesian Codes constructed using two different generalized Reed-Solomon codes

Oisin Campion·Fernando Hernando·Gary McGuire
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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.

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Oisin Campion, Fernando Hernando, Gary McGuire. 2025-12-18. New Quantum Stabilizer Codes from generalized Monomial-Cartesian Codes constructed using two different generalized Reed-Solomon codes. https://arxiv.org/abs/2512.16482

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