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Symmetric Hadamard matrices of order 116 and 172 exist
Olivia Di Matteo, Dragomir Z. Djokovic, Ilias S. Kotsireas
We construct new symmetric Hadamard matrices of orders , and . While the existence of those of order was known since 1978, the orders and are new. Our…
Periodic Golay pairs of length 72
Dragomir Z. Djokovic, Ilias S. Kotsireas
We construct supplementary difference sets (SDS) with parameters . These SDSs give periodic Golay pairs of length 72. No periodic Golay pair of length 72 was known p…
Some new periodic Golay pairs
Dragomir Z. Djokovic, Ilias S. Kotsireas
Periodic Golay pairs are a generalization of ordinary Golay pairs. They can be used to construct Hadamard matrices. A positive integer is a (periodic) Golay number if there exi…
Compression of Periodic Complementary Sequences and Applications
Dragomir Z. Djokovic, Ilias S. Kotsireas
A collection of complex sequences of length v is complementary if the sum of their periodic autocorrelation function values at all non-zero shifts is constant. For a complex sequen…
New results on D-optimal Matrices
Dragomir Z. Djokovic, Ilias S. Kotsireas
We construct a number of new (v;r,s;lambda) supplementary difference sets (SDS) with v odd and lambda = (r+s)-(v-1)/2. In particular, these give rise to D-optimal matrices of the f…
Supplementary difference sets with symmetry for Hadamard matrices
Dragomir Z. Djokovic
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_…