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A new construction for Williamson-type matrices

Journal Article


Abstract


  • It is shown that if q is a prime power then there are Williamson-type matrices of order (i) 1/2 q2(q + 1) when q ≡ 1 (mod 4). (ii) 1/4 q2(q + 1) when q ≡ 3 (mod 4) and there are Williamson-type matrices of order 1/4(q + 1). This gives Williamson-type matrices for the new orders 363, 1183, 1805, 2601, 3174, 5103. The construction can be combined with known results on orthogonal designs to give an Hadamard matrix of the new order 33396 = 4 {dot operator} 8349. © 1986 Springer-Verlag.

Publication Date


  • 1986

Citation


  • Seberry, J. (1986). A new construction for Williamson-type matrices. Graphs and Combinatorics, 2(1), 81-87. doi:10.1007/BF01788080

Scopus Eid


  • 2-s2.0-34250129133

Web Of Science Accession Number


Start Page


  • 81

End Page


  • 87

Volume


  • 2

Issue


  • 1

Abstract


  • It is shown that if q is a prime power then there are Williamson-type matrices of order (i) 1/2 q2(q + 1) when q ≡ 1 (mod 4). (ii) 1/4 q2(q + 1) when q ≡ 3 (mod 4) and there are Williamson-type matrices of order 1/4(q + 1). This gives Williamson-type matrices for the new orders 363, 1183, 1805, 2601, 3174, 5103. The construction can be combined with known results on orthogonal designs to give an Hadamard matrix of the new order 33396 = 4 {dot operator} 8349. © 1986 Springer-Verlag.

Publication Date


  • 1986

Citation


  • Seberry, J. (1986). A new construction for Williamson-type matrices. Graphs and Combinatorics, 2(1), 81-87. doi:10.1007/BF01788080

Scopus Eid


  • 2-s2.0-34250129133

Web Of Science Accession Number


Start Page


  • 81

End Page


  • 87

Volume


  • 2

Issue


  • 1