Designs, Codes and Cryptography

, Volume 58, Issue 1, pp 1-9

First online:

An equivalence of Ward’s bound and its application

  • Xiaoyu LiuAffiliated withDepartment of Mathematics and Statistics, Wright State University Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.


Divisible codes Ward’s bound

Mathematics Subject Classification (2000)