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New Hadamard matrices and conference matrices obtained via Mathon's construction

Journal Article


Abstract


  • We give a formulation, via (1, -1) matrices, of Mathon's construction for conference matrices and derive a new family of conference matrices of order 5{dot operator}92 t+1 + 1, t ≥ 0. This family produces a new conference matrix of order 3646 and a new Hadamard matrix of order 7292. In addition we construct new families of Hadamard matrices of orders 6{dot operator}92 t+1 + 2, 10{dot operator}92 t+1 + 2, 8{dot operator}49{dot operator}9t, t ≥ 0;q2(q + 3) + 2 where q ≡ 3 (mod 4) is a prime power and 1/2(q + 5) is the order of a skew-Hadamard matrix); (q + 1)q2{dot operator}9t, t ≥ 0 (where q ≡ 7 (mod 8) is a prime power and 1/2(q + 1) is the order of an Hadamard matrix). We also give new constructions for Hadamard matrices of order 4{dot operator}9t ≥ 0 and (q + 1)q2 (where q ≡ 3 (mod 4) is a prime power). © 1988 Springer-Verlag.

Publication Date


  • 1988

Citation


  • Seberry, J., & Whiteman, A. L. (1988). New Hadamard matrices and conference matrices obtained via Mathon's construction. Graphs and Combinatorics, 4(1), 355-377. doi:10.1007/BF01864173

Scopus Eid


  • 2-s2.0-0038957832

Web Of Science Accession Number


Start Page


  • 355

End Page


  • 377

Volume


  • 4

Issue


  • 1

Abstract


  • We give a formulation, via (1, -1) matrices, of Mathon's construction for conference matrices and derive a new family of conference matrices of order 5{dot operator}92 t+1 + 1, t ≥ 0. This family produces a new conference matrix of order 3646 and a new Hadamard matrix of order 7292. In addition we construct new families of Hadamard matrices of orders 6{dot operator}92 t+1 + 2, 10{dot operator}92 t+1 + 2, 8{dot operator}49{dot operator}9t, t ≥ 0;q2(q + 3) + 2 where q ≡ 3 (mod 4) is a prime power and 1/2(q + 5) is the order of a skew-Hadamard matrix); (q + 1)q2{dot operator}9t, t ≥ 0 (where q ≡ 7 (mod 8) is a prime power and 1/2(q + 1) is the order of an Hadamard matrix). We also give new constructions for Hadamard matrices of order 4{dot operator}9t ≥ 0 and (q + 1)q2 (where q ≡ 3 (mod 4) is a prime power). © 1988 Springer-Verlag.

Publication Date


  • 1988

Citation


  • Seberry, J., & Whiteman, A. L. (1988). New Hadamard matrices and conference matrices obtained via Mathon's construction. Graphs and Combinatorics, 4(1), 355-377. doi:10.1007/BF01864173

Scopus Eid


  • 2-s2.0-0038957832

Web Of Science Accession Number


Start Page


  • 355

End Page


  • 377

Volume


  • 4

Issue


  • 1