Let

be a binary linear

-code defined by a check matrix

with columns

, and let

if

, and

if

. A combinatorial argument relates the Walsh transform of

with the weight distribution

of the code

for small

. This leads to another proof of the Pless

th power moment identities for

. This relation also provides a simple method for computing the weight distribution

for small

. The implementation of this method requires at most

additions and subtractions,

.

multiplications, and

memory cells. The method may be very effective if there is an analytic expression for the characteristic Boolean function

. This situation will be illustrated by several examples.