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A class of cyclic (v; k1, k2, k3; λ) difference families with v ≡ 3 (mod 4) a prime

Dragomir Ž. Ðokovic;  Ilias S. Kotsireas — 2016

Special Matrices

We construct several new cyclic (v; k1, k2, k3; λ) difference families, with v ≡ 3 (mod 4) a prime and λ = k1 + k2 + k3 − (3v − 1)/4. Such families can be used in conjunction with the well-known Paley-Todd difference sets to construct skew-Hadamard matrices of order 4v. Our main result is that we have constructed for the first time the examples of skew Hadamard matrices of orders 4 · 239 = 956 and 4 · 331 = 1324.

Symmetric Hadamard matrices of order 116 and 172 exist

Olivia Di Matteo;  Dragomir Ž. Ðoković;  Ilias S. Kotsireas — 2015

Special Matrices

We construct new symmetric Hadamard matrices of orders 92, 116, and 172. While the existence of those of order 92 was known since 1978, the orders 116 and 172 are new. Our construction is based on a recent new combinatorial array (GP array) discovered by N. A. Balonin and J. Seberry. For order 116 we used an adaptation of an algorithm for parallel collision search. The adaptation pertains to the modification of some aspects of the algorithm to make it suitable to solve a 3-way matching problem....

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