Further results on base sequences, disjoint complementary sequences, OD(4t; t, t, t, t) and the excess of Hadamard matrices
 Publication Year:
 1990

 Bepress 115

 Bepress 12
 Repository URL:
 https://ro.uow.edu.au/infopapers/1100
 Author(s):
 Tags:
 Physical Sciences and Mathematics
article description
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 nonperiodic (periodic) auto correlation function to form longer sequences. We give an alternate construction for Tsequences of length (4n + 3)(2m + p) where n is the length of a Yang nice sequence. These results are then used in the GoethalsSeidel or (Seberry) WallisWhiteman 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.