The Generalized Reed-Muller Codes in a Modular Group Algebra
Harinaivo Andriatahiny *
Mention: Mathematics and Computer Science, Domain: Sciences and Technologies, University of Antananarivo, Madagascar.
Vololona Harinoro Rakotomalala
Mention: Meteorology, Domain: Sciences of the Engineer, Higher Polytechnic School of Antananarivo (ESPA), University of Antananarivo, Madagascar.
*Author to whom correspondence should be addressed.
Abstract
We study some properties of the modular group algebra of the additive group of a Galois ring over a finite field. A description of the Generalized Reed-Muller codes in this group algebra is presented.
Keywords: Generalized Reed-Muller codes, group algebra, galois ring, jennings basis