New D-optimal designs via cyclotomy and generalised cyclotomy

@article{Gysin1997NewDD,
  title={New D-optimal designs via cyclotomy and generalised cyclotomy},
  author={Marc Gysin},
  journal={Australasian J. Combinatorics},
  year={1997},
  volume={15},
  pages={247-256}
}
  • Marc Gysin
  • Published 1997 in Australasian J. Combinatorics
D-optimal designs are n x n ±l-matrices where n == 2 mod 4 with maximum determinant. D-optimal designs obtained via circulant matrices are equivalent to 2-{ v; kl i k2 i k1 + k2 ~(v 1)} supplementary difference sets, where v = ~. We use cyclotomy to construct D-optimal designs, where v is a prime. We give a generalisation of cyclotomy and extend the cyclotomic techniques which enables use to find new D-optimal designs for composite numbers. In particular, we found, via computer-search, D… CONTINUE READING

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References

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Showing 1-8 of 8 references

Cyclotomy, Hadamard arrays and supplementary difference sets

D. Hunt, J. S. Wallis
Proceedings of the Second Manitoba Conference on Numerical Mathematics, Congressus Numerantium VII, Manitoba, • 1972
View 4 Excerpts
Highly Influenced

On maximal (1, -I)-matrices of order 2n, n odd

D. Z. Dokovic
Radovi Matematicki, • 1991

On determinants with elements ±1 II, Bulletin of the London

J.H.E. Cohn
Mathematical Society, • 1989
View 1 Excerpt

Orthogonal Designs, Quadratic Forms and Hadamard Matrices

A. V. Geramita, J. Seberry
1979
View 1 Excerpt

Determinantenabschatzungen fur binare Matrizen

H. Ehlich
Mathematische Zeitschrift, • 1964
View 1 Excerpt

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