The Generalized Reed-Muller Codes and the Radical Powers of a Modular Algebra
Harinaivo Andriatahiny *
Mention of Mathematics and Computer Science, Domain of Sciences and Technologies, University of Antananarivo, P.O.B. 906, 101 Antananarivo, Madagascar.
*Author to whom correspondence should be addressed.
Abstract
S.D. Berman and P. Charpin characterized the Reed-Muller codes over the binary field or over an arbitrary prime field as the powers of the radical in a modular group algebra. We present a new proof of this famous theorem. Furthermore, the same method is used for the study of the Generalized Reed-Muller codes over a non prime field.
Keywords: Generalized Reed-Muller codes, modular algebra, nilpotent radical, interpolation function