A new proof of Delsarte, Goethals and Mac Williams theorem on minimal weight codewords of generalized Reed-Muller code

TL;DR

This paper presents a novel proof of a classical theorem on minimal weight codewords in generalized Reed-Muller codes, using support intersection analysis and recursive methods.

Contribution

It introduces a new proof technique for the theorem, focusing on support intersections with affine hyperplanes and recursive reasoning.

Findings

Provides a new proof of the theorem from 1970

Uses intersection of support with affine hyperplanes

Employs recursive proof strategy

Abstract

We give a new proof of Delsarte, Goethals and Mac williams theorem on minimal weight codewords of generalized Reed-Muller codes published in 1970. To prove this theorem, we consider intersection of support of minimal weight codewords with affine hyperplanes and we proceed by recursion.