Supplementary difference sets with symmetry for Hadamard matrices

Details Supplementary difference sets with symmetry for Hadamard matrices Supplementary difference sets with symmetry for Hadamard matrices

2009-03-29

arxiv.org/abs/0903.5053v2

Operators and Matrices, vol. 3, No. 4 (2009), 557-569.

Mathematics

Combinatorics

16 pages, 2 tables. A few minor changes are made. The paper will appear in Operators and Matrices

Scientific paper

First we give an overview of the known supplementary difference sets (SDS) (A_i), i=1..4, with parameters (n;k_i;d), where k_i=|A_i| and each A_i is either symmetric or skew and k_1 + ... + k_4 = n + d. Five new Williamson matrices over the elementary abelian groups of order 25, 27 and 49 are constructed. New examples of skew Hadamard matrices of order 4n for n=47,61,127 are presented. The last of these is obtained from a (127,57,76)-difference family that we have constructed. An old non-published example of G-matrices of order 37 is also included.

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