Weight polarization and divisibility
type: Item
instance of: scholarly article
title: Weight polarization and divisibility
zbMATH Open document ID: 0714.94012
DOI: 10.1016/0012-365X(90)90015-A
author: Harold N. Ward
published in: Discrete Mathematics
publication date: 1990-01-01T00:00:00Z
review text: This paper develops the polarization of the weight function and presents a test for divisibility of a code that can be carried out on a given spanning set. The paper includes another proof of the theorem of \textit{J. Ax} [Am. J. Math. 86, 255--261 (1964; Zbl 0121.02003)] on divisors of weights of polynomial functions. The paper concludes with an application to Reed-Muller codes that leads to Ax's theorem.
reviewed by: Bai Kishan Dass
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 4176975
zbMATH Keywords: linear code
zbMATH Keywords: divisibility test
zbMATH Keywords: polarization
zbMATH Keywords: weight function
zbMATH Keywords: divisors of weights of polynomial functions
zbMATH Keywords: Reed-Muller codes
MaRDI profile type: Publication
cites work: Zeroes of Polynomials Over Finite Fields
cites work: Q3726220
cites work: On generalized ReedMuller codes and their relatives
cites work: Q3939714
cites work: Q3851094
cites work: Notes on Binomial Coefficients I-A Generalization of Lucas' Congruence†
cites work: Q3665189
cites work: Combinatorial polarization
cites work: Divisible codes
cites work: MULTILINEAR FORMS AND DIVISORS OF CODEWORD WEIGHTS
Wikidata QID: Q127773993
description: scientific article; zbMATH DE number 4176975