Abstract
We obtain new base sequences, that is four sequences of lengths m + p, m + p, m, m, with p odd, which have zero auto correlation function which can be used with Yang numbers and four disjoint complementary sequences (and matrices) with zero non-periodic (periodic) auto correlation function to form longer sequences. We give an alternate construction for T-sequences of length (4n + 3)(2m + p) where n is the length of a Yang nice sequence. These results are then used in the Goethals-Seidel or (Seberry) Wallis-Whiteman construction to determine eight possible decompositions into squares of (4n + 3) (2m + p) in terms of the decomposition into squares of 2 m + 1 when there are four suitable sequences of lengths m + 1, m + 1, m, m and m, the order of four Williamson type matrices. The new results thus obtained are tabulated giving OD(4t; t, t, t, t) for the new orders t є{121, 135, 217, 221, 225, 231, 243, 245, 247, 253, 255, 259, 261, 265, 273, 275, 279, 285, 287, 289, 29S, 297, 299}. The Hadamard matrix with greatest known excess for these new t is then listed.
Publication Details
Koukouvinos, C, Kounias, S and Seberry, J, Further results on base sequences, disjoint complementary sequences, OD(4t; t, t, t, t) and the excess of Hadamard matrices, Ars Combinatoria, 30, 1990, 241-256.