Generalized hyperderivative Reed–Solomon codes

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.