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A new construction for Williamson-type matrices

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Abstract

It is shown that ifq is a prime power then there are Williamson-type matrices of order

  1. (i)

    1/2q 2(q + 1) whenq ≡ 1 (mod 4).

  2. (ii)

    1/4q 2(q + 1) whenq ≡ 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 ⋅ 8349.

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Authors and Affiliations

  1. Department of Computer Science, University of Sydney, 2006, N.S.W., Australia

    Jennifer Seberry

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  1. Jennifer Seberry
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This research was supported in part by an ARGS grant.

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

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  • DOI: https://doi.org/10.1007/BF01788080

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