Supplementary difference sets with symmetry for Hadamard matrices
Combinatorics
2010-02-14 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0903.5053,
title = {Supplementary difference sets with symmetry for Hadamard matrices},
author = {Dragomir Z. Djokovic},
journal= {arXiv preprint arXiv:0903.5053},
year = {2010}
}
Comments
16 pages, 2 tables. A few minor changes are made. The paper will appear in Operators and Matrices