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In 1970 Delsarte, Goethals and Mac Williams published a seminal paper ongeneralized Reed-Muller codes where, among many important results, they provedthat the minimal weight codewords of these codes are obtained through theevaluation of certain polynomials which are a specific product of linearfactors, which they describe. In the present paper we extend this result to aclass of Reed-Muller type codes defined on a product of (possibly distinct)finite fields of the same characteristic. The paper also brings an expositorysection on the study of the structure of low weight codewords, not only foraffine Reed-Muller type codes, but also for the projective ones.

An extension of Delsarte, Goethals and Mac Williams theorem on minimal weight codewords to a class of Reed-Muller type codes