The Generalized Reed-Muller codes and the radical powers of a modular   algebra
  First, a new proof of Berman and Charpin's characterization of the Reed-Muller codes over the binary field or over an arbitrary prime field is presented. These codes are considered as the powers of the radical of a modular algebra. Secondly, the same method is used for the study of the Generalized Reed-Muller codes over a non prime field. 
Harinaivo Andriatahiny
cs.IT math.IT