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

Jennifer Seberry | Zendy

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

Author(s) -

Jennifer Seberry

Publication year - 1989

Publication title -

graphs and combinatorics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.59

H-Index - 40

eISSN - 1435-5914

pISSN - 0911-0119

DOI - 10.1007/bf01788694

Subject(s) - hadamard transform , mathematics , hadamard matrix , combinatorics , order (exchange) , hadamard's inequality , hadamard's maximal determinant problem , complex hadamard matrix , matrix (chemical analysis) , block (permutation group theory) , hadamard three lines theorem , mathematical analysis , materials science , composite material , finance , economics

We show that anSBIBD(4k 2, 2k 2 +k,k 2 +k) is equivalent to a regular Hadamard matrix of order 4k 2 which is equivalent to an Hadamard matrix of order 4k 2 with maximal excess. We find many newSBIBD(4k 2, 2k 2 +k,k 2 +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, 32m , 25⋅32m ,m ≥ 0}.

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