On the matrices used to construct Baumert-Hall arrays

Authors

Richard B. Lakein
Jennifer Seberry, University of WollongongFollow

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.

Abstract

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 X_i and such that

X₁X₁^T+ X₂X₂^T + X₃X₃^T + X₄X₄^T = tI_t

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.