On the Complete Pivoting Conjecture for Hadamard Matrices of Order 16

摘要

In this paper we study explicitly the pivot structure of the Hadamard matrices of order 16. We examine for each representative of the five equivalent classes the appearing pivot structures and we give tables summarising the attained 34 different structures. We give ten examples of 16 x 16 Hadamard matrices all coming from Class I, for which when Gaussian Elimination with complete pivoting is applied on them, the fourth last pivot is 16/2.