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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.