SBIBD(4k 2, 2k 2 +k,k 2 +k) and Hadamard matrices of order 4k 2 with maximal excess are equivalent期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

SBIBD(4k 2, 2k 2 +k,k 2 +k) and Hadamard matrices of order 4k 2 with maximal excess are equivalent

Authors:	Jennifer Seberry

Affiliation:	(1) Department of Computer Science, University College, The University of New South Wales, Australian Defence Force Academy, 2600 Canberra, ACT, Australia

Abstract:	We show that anSBIBD(4k², 2k² +k,k² +k) is equivalent to a regular Hadamard matrix of order 4k² which is equivalent to an Hadamard matrix of order 4k² with maximal excess.We find many newSBIBD(4k², 2k² +k,k² +k) including those for evenk when there is an Hadamard matrix of order 2k (in particular all 2k 210) andk {1, 3, 5,..., 29, 33,..., 41, 45, 51, 53, 61,..., 69, 75, 81, 83, 89, 95, 99, 625, 3^2m, 253^2m,m 0}.

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