Classify weighing matrices of order 19 and weight 9

Classify all weighing matrices of order 19 and weight 9 up to the equivalence relation defined by monomial transformations.

Background

The paper studies mutually unbiased weighing matrices of weight 9 by enumerating inequivalent weighing matrices and then applying ternary-code and clique methods. Complete classifications are available only for orders up to 18 in the range relevant to the computations. For order 19, the authors construct examples from ternary maximal self-orthogonal codes and find a set containing six mutually unbiased weighing matrices, but they do not have a classification of all weighing matrices of that order and weight.