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.
@article{bwmeta1.element.doi-10_1515_spma-2016-0029,
author = {Dragomir Z. Dokovic and Ilias S. Kotsireas},
title = {A class of cyclic (v; k1, k2, k3; l) difference families with v [?] 3 (mod 4) a prime},
journal = {Special Matrices},
volume = {4},
year = {2016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2016-0029}
}
Dragomir Ž. Ðokovic; Ilias S. Kotsireas. A class of cyclic (v; k1, k2, k3; λ) difference families with v ≡ 3 (mod 4) a prime. Special Matrices, Tome 4 (2016) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2016-0029/