2025/12/28 by Can, Mahir Bilen, Horowitz, Benjamin
#FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2512.22948
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.