On unit weighing matrices with small weight

Darcy Best, Hadi Kharaghani, Hugh Ramp

Published 2012-09-20, updated 2012-12-10Version 2

We study the structure of unit weighing matrices of order n and weights 2, 3 and 4. We show that the number of inequivalent unit weighing matrices UW(n,4) depends on the number of decompositions of n into sums of non-negative multiples of some specific positive integers. We also show two interesting sporadic cases in order to show the complexities involved for weights larger than 4.