Publication Details

Richard B. Lakein and Jennifer Seberry Wallis, On the matrices used to construct Baumert-Hall arrays, Combinatorics: III, Lecture Notes in Mathematics, 452, Springer--Verlag, Berlin--Heidelberg--New York, (1975), 156-170.


Four circulant (or type 1) (0,1,-1) matrices X1, X2, X3, X4 of order t with the property that each of the t2 positions is non-zero in precisely one of the Xi and such that

X1X1T+ X2X2T + X3X3T + X4X4T = tIt

will be called T-matrices.

This paper studies the construction, use and properties of T-matrices giving a new construction for Hadamard matrices and some new equivalence results for Hadamard matrices and Baumert-Hall arrays.