Addendum to further results on base sequences, disjoint complementary sequences, OD(4t; t, t, t, t) and the excess of Hadamard matrices

Authors

Christos Koukouvinos
Jennifer Seberry, University of WollongongFollow

Publication Details

Christos Koukouvinos and Jennifer Seberry, Addendum to further results on base sequences, disjoint complementary sequences, OD(4t; t, t, t, t) and the excess of Hadamard matrices, Twenty-Second Southeastern Conference on Combinatorics, Graph Theory and Computing, and Congressus Numerantium, 82, (1991), 97-103.

Abstract

It is known that if there are base sequences of lengths m + p, m + p, m, m and y is a Yang number then there are T-sequences of length (2m + p)y.

Let G = {g : g = 2^a10^b26^c, a, b, c non negative integers}. We show that base sequences currently exist for p = 1 and m ∑{I, ... , 18,20,21,23,25, 29} U G. Yang numbers currently exist for y ∑ {3, 5, ... ,33,37,41,45,51,53,59,65,81, ... and 2g + 1 > 81, g ∑ G}. This means T-sequences exist for

0₁ = {t : t odd ≤ 59} U {s : 63 ≤ s ≤ 199,s not prime, s ≠ 183}

0₂ = {ym : y a Yang number, m a base sequence}

0₃ = {g + g' : g,g'∑ G(e.g. we may take g' = 1)}

E₁ = {2yp : y a Yang number and p ∑ 0₁ U 0₂ U 0₃ U E₁. In particular we find a new SBIBD(4k², 2k² + k, k² + k) for k = 43, and new Hadamard matrices with maximum known excess for n = 860 and 1204.