English

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}
}
R2 v1 2026-07-01T08:31:18.930Z