Generalized Hyperderivative Reed-Solomon Codes
Information Theory
2025-12-30 v1 math.IT
Rings and Algebras
Abstract
This article introduces Generalized Hyperderivative Reed-Solomon codes (GHRS codes), which generalize NRT Reed-Solomon codes. Its main results are as follows: 1) every GHRS code is MDS, 2) the dual of a GHRS code is also an GHRS code, 3) determine subfamilies of GHRS codes whose members are low-density parity-check codes (LDPCs), and 4) determine a family of GHRS codes whose members are quasi-cyclic. We point out that there are GHRS codes having all of these properties.
Cite
@article{arxiv.2512.22948,
title = {Generalized Hyperderivative Reed-Solomon Codes},
author = {Mahir Bilen Can and Benjamin Horowitz},
journal= {arXiv preprint arXiv:2512.22948},
year = {2025}
}