On unit weighing matrices with small weight

The structure of unit weighing matrices of order nn and weights 2, 3 and 4 is studied. We show that the number of inequivalent unit weighing matrices UW(n,4)UW(n,4) depends on the number of decomposition of nn into sums of non-negative multiples of some specific positive integers. Two interesting sporadic cases are presented in order to demonstrate the complexities involved in the classification of weights larger than 4.