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arXiv · 2501.17010

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

Oisin Campion·Fernando Hernando·Gary McGuire
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Abstract

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

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Oisin Campion, Fernando Hernando, Gary McGuire. 2025-01-28. New Quantum MDS Codes with Flexible Parameters from Hermitian Self-Orthogonal GRS Codes. https://doi.org/10.1007/s12095-025-00834-2

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