On the pivot structure for the weighing matrix W(12,11)

C. Koukouvinos, M. Mitrouli and Jennifer Seberry, in "Growth in Gaussian elimination for weighing matrices, W(n, n — 1)", Linear Algebra and its Appl., 306 (2000), 189-202, conjectured that the growth factor for Gaussian elimination of any completely pivoted weighing matrix of order n and weight n — 1 is n — 1 and that the first and last few pivots are (1, 2, 2, 3 or 4, ... , n — 1 or n — 1) for n > 14. In the present paper we concentrate our study on the growth problem for the weighing matrix W(12, 11) and we show that the unique W(12,11) has three pivot structures.