Weights Modulo a Prime Power in Divisible Codes and a Related Bound

In this paper, we generalize the theorem given by R. M. Wilson about weights modulo
$p^t$
in linear codes to a divisible code version. Using a similar idea, we give an upper bound for the dimension of a divisible code by some divisibility property of its weight enumerator modulo
$p^e$
. We also prove that this bound implies Ward's bound for divisible codes. Moreover, we see that in some cases, our bound gives better results than Ward's bound.