Abstract
Recent advances in the construction of Hadamard matrices have depended on the existence of Baumert-Hall arrays and Williamson-type matrices. These latter are four (1,-1) matrices A,B,C,D, of order m, which pairwise satisfy (i) MNT = NMT, M,N ε {A,B,C,D}, and (ii) AAT+BBT+CCT+DDT = 4mIm, where I is the identity matrix. Currently Williamson matrices are known to exist for all orders less than 100 except: 35,39,47,53,59,65,67,70,71,73,76,77,83,89,94. This paper gives two constructions for Williamson matrices of even order, 2n. This is most significant when no Williamson matrices of order n are known. In particular we give matrices for the new orders 2.39,2.203,2.303,2.333,2.689,2.915, 2.1603.
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© 1974 Springer-Verlag
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Wallis, J.S. (1974). Williamson matrices of even order. In: Holton, D.A. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0057387
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DOI: https://doi.org/10.1007/BFb0057387
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