Designs, Codes and Cryptography

, Volume 58, Issue 1, pp 1–9

An equivalence of Ward’s bound and its application

Article

DOI: 10.1007/s10623-010-9380-1

Cite this article as:
Liu, X. Des. Codes Cryptogr. (2011) 58: 1. doi:10.1007/s10623-010-9380-1
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Abstract

It is well known that the MacWilliams transform of the weight enumerator of some code having integer coefficients is equivalent to a set of congruences having integer solutions. In this paper, we prove an equivalent condition of Ward’s bound on dimension of divisible codes, which is part of this set of congruences having integer solutions. This new interpretation makes the generalization of Ward’s bound an explicit one.

Keywords

Divisible codesWard’s bound

Mathematics Subject Classification (2000)

94B05

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsWright State UniversityDaytonUSA