A search for solvable weighing matrices

A weighing matrix W(n, k) of order n with weight k is an n × n matrix with entries from {0, 1, - 1} which satisfies WW^T = kI_n. Such a matrix is group-developed if its rows and columns can be indexed by elements of a finite group G so that ω _g,h = ω_{gf, hf} for all g, h, and f in G. Group-developed weighing matrices are a natural generalization of perfect ternary arrays and Hadamard matrices. They are closely related to difference sets. We describe a search for weighing matrices with order 60 and weight 25, developed over solvable groups. There is one known example of a W(60, 25) developed over a nonsolvable group; no solvable examples are known. We use techniques from representation theory, including a new viewpoint on complementary quotient images, to restrict solvable examples. We describe a computer search strategy which has eliminated two of twelve possible cases. We summarize plans to complete the search.