Treffer: A lemma on polynomials modulo pm and applications to coding theory
Title:
A lemma on polynomials modulo pm and applications to coding theory
Authors:
Source:
International workshop on combinatorics, linear algebra, and graph coloringDiscrete mathematics. 306(23):3154-3165
Publisher Information:
Amsterdam: Elsevier, 2006.
Publication Year:
2006
Physical Description:
print, 11 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Combinatoire, Combinatorics, Problèmes combinatoires classiques, Classical combinatorial problems, Algèbre, Algebra, Théorie des nombres, Number theory, Code cyclique, Cyclic code, Código cíclico, Code linéaire, Linear code, Código lineal, Congruence, Congruencia, Fonction polynomiale, Polynomial function, Función polinomial, Nombre entier, Integer, Entero, Polynôme, Polynomial, Polinomio, Puissance, Power, Potencia, Théorie codage, Coding theory, Teoría codificación, Ax-Katz, Classe congruence, Divisibilité, McEliece, Poids, Weight, Preuve théorème, 05A10, 11B50, 11T06, 11T71, Codes, Polynomials, Weights
Document Type:
Konferenz
Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics 253-37, California Institute of Technology, Pasadena, CA 91125, United States
ISSN:
0012-365X
Rights:
Copyright 2007 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.18288818
Database:
PASCAL Archive
Weitere Informationen
An integer-valued function f(x) on the integers that is periodic of period pe, p prime, can be matched, modulo pm, by a polynomial function w(x); we show that w(x) may be taken to have degree at most (m(p - 1) + 1 ) pe-1 - 1. Applications include a short proof of the theorem of McEliece on the divisibility of weights of codewords in p-ary cyclic codes by powers of p, an elementary proof of the Ax-Katz theorem on solutions of congruences modulo p, and results on the numbers of codewords in p-ary linear codes with weights in a given congruence class modulo pe.