Existence of SBIBD(4k2, 2k2 + k, k2 + k) and Hadamard matrices with maximal excess

Authors

Jennifer Seberry, University of WollongongFollow

Publication Details

Jennifer Seberry, Existence of SBIBD(4k², 2k² + k, k² + k) and Hadamard matrices with maximal excess, Australian Journal of Combinatorics, 4, (1991), 87-92.

Abstract

It is shown that SBIBD( 4k², 2k² ± k, k² ± k) and Hadamard matrices with maximal excess exist for k = qs, q ∑{q : q ≡ 1 (mod 4) is a prime power}, s ∑ {I, ... ,33, 37, ... ,41,45, ... ,59} U {2g + 1,g the length of a Golay sequence}.

This leaves the following odd k < 250 undecided 47,71,77,79,103,107;127,131,133,139, 141,151,163,167,177,179,191,199,209, ... ,217,223,227, 231,233,237,239,243,249. There is also a proper n dimensional Hadamard matrix of order (4k²)ⁿ. Regular symmetric Hadamard matrices with constant diagonal are obtained for orders 4k² whenever complete regular 4-sets of regular matrices of order k2 exist.