New Quantum Stabilizer Codes from generalized Monomial-Cartesian Codes constructed using two different generalized Reed-Solomon codes
Oisin Campion, Fernando Hernando, Gary McGuire
TL;DR
This paper introduces Generalized Monomial Cartesian Codes (GMCC), extending Reed-Solomon codes, and demonstrates how combining two such codes can produce quantum stabilizer codes with Hermitian self-orthogonality.
Contribution
It presents a novel class of quantum stabilizer codes derived from GMCC, constructed using two different generalized Reed-Solomon codes, with conditions for Hermitian self-orthogonality.
Findings
GMCC generalizes Reed-Solomon codes.
Conditions for Hermitian self-orthogonality are established.
New quantum codes are constructed from GMCC.
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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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Coding theory and cryptography · Polynomial and algebraic computation