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

**2016-01-28**

1601.07633 | cs.IT

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.

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