2019/03/22 by Cícero Carvalho, Carvalho, Cicero, Víctor Neumann +1
Computer Science · Social Sciences · #14G50 #94B27 #Algebraic Geometry (math.AG) #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Mathematics #Islamic Finance and Communication
paper · pdf · doi:10.48550/arxiv.1903.09458
openalex publication_date 2019/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.