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

Journal Article


Abstract

  • We show that an SBIBD(4 k2, 2 k2 +k, k2 +k) is equivalent to a regular Hadamard matrix of order 4 k2 which is equivalent to an Hadamard matrix of order 4 k2 with maximal excess. We find many new SBIBD(4 k2, 2 k2 +k, k2 +k) including those for even k when there is an Hadamard matrix of order 2 k (in particular all 2 k ≤ 210) and k ∈ {1, 3, 5,..., 29, 33,..., 41, 45, 51, 53, 61,..., 69, 75, 81, 83, 89, 95, 99, 625, 32 m, 25{dot operator}32 m, m ≥ 0}. © 1989 Springer-Verlag.

Publication Date

  • 1989

Citation

  • SBIBD(4 k2, 2 k2 +k, k2 +k) and Hadamard matrices of order 4 k2 with maximal excess are equivalent (1989). Graphs and Combinatorics, 5(1), 373-383. doi:10.1007/BF01788694

Scopus Eid

  • 2-s2.0-34249968341

Web Of Science Accession Number

Start Page

  • 373

End Page

  • 383

Volume

  • 5

Issue

  • 1

Abstract

  • We show that an SBIBD(4 k2, 2 k2 +k, k2 +k) is equivalent to a regular Hadamard matrix of order 4 k2 which is equivalent to an Hadamard matrix of order 4 k2 with maximal excess. We find many new SBIBD(4 k2, 2 k2 +k, k2 +k) including those for even k when there is an Hadamard matrix of order 2 k (in particular all 2 k ≤ 210) and k ∈ {1, 3, 5,..., 29, 33,..., 41, 45, 51, 53, 61,..., 69, 75, 81, 83, 89, 95, 99, 625, 32 m, 25{dot operator}32 m, m ≥ 0}. © 1989 Springer-Verlag.

Publication Date

  • 1989

Citation

  • SBIBD(4 k2, 2 k2 +k, k2 +k) and Hadamard matrices of order 4 k2 with maximal excess are equivalent (1989). Graphs and Combinatorics, 5(1), 373-383. doi:10.1007/BF01788694

Scopus Eid

  • 2-s2.0-34249968341

Web Of Science Accession Number

Start Page

  • 373

End Page

  • 383

Volume

  • 5

Issue

  • 1