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The Generalized Reed-Muller codes and the radical powers of a modular algebra

Research paper by Harinaivo Andriatahiny

Indexed on: 27 Jan '16Published on: 27 Jan '16Published in: Computer Science - Information Theory



Abstract

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.