1998•IEEE Transactions on Information TheoryRequires access

Cyclic subcodes of generalized Reed-Muller codes

Óscar Moreno, Iwan Duursma, Jean-Pierre Cherdieu, A. Edouard

Abstract

We consider certain subcodes of generalized Reed-Muller (GRM) codes, which we call homogeneous generalized Reed-Muller (HRM) codes. In general, they have a much better minimum distance than the GRM codes. The parameters of HRM codes are related to those of projective Reed-Muller (PRM) codes. Unlike most PRM codes, punctured HRM codes are cyclic. Under the trace map, HRM codes map to binary codes. These are in general much larger than classical RM codes, for the same minimum distance.

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Key concepts: Reed–Muller code, Block code, Linear code, Mathematics, Concatenated error correction code, Raptor code, Expander code, Minimum distance