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