arXiv subjects

Oisin Campion

Publications and source records attributed to Oisin Campion.

3 recordsLinked to original sources

arXiv2025

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

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.

cs.IT↗

arXiv2025

Hermitian hull of some GRS codes and new EAQMDS codes

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.

cs.IT↗

arXiv2025

New Quantum MDS Codes with Flexible Parameters from Hermitian Self-Orthogonal GRS Codes

Let $q$ be a prime power. Let $λ>1$ be a divisor of $q-1$, and let $τ>1$ and $ρ>1$ be divisors of $q+1$. Under certain conditions we prove that there exists an MDS stabilizer quantum code with length $n=λτσ$ where $2\le σ\le ρ$. This is a flexible construction, which includes new MDS parameters not known before.

cs.IT↗