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

Elodie Leducq (1)

1 IMJ - Institut de Mathématiques de Jussieu

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.

Mots clés: generalized Reed-Muller Codes; minimal weight; hyperplane

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Elodie Leducq. A new proof of Delsarte, Goethals and Mac Williams theorem on minimal weight codewords of generalized Reed-Muller code. 2010. ⟨hal-00446913⟩