The Solution of the Waterloo Problem

@article{Arasu1995TheSO,
  title={The Solution of the Waterloo Problem},
  author={K. Arasu and J. Dillon and D. Jungnickel and A. Pott},
  journal={J. Comb. Theory, Ser. A},
  year={1995},
  volume={71},
  pages={316-331}
}
Abstract Let D(d, q) be a classical (ν, k, λ)-Singer difference set in a cyclic group G corresponding to the complement of the point-hyperplane design of PG(d, q) (d ⩾ 1). We characterize those Singer difference sets D(d, q) which admit a “Waterloo decomposition” D = A ∪ B such that (A − B) · (A − B)(−1) = k in Z G: Theorem. D(d, q) admits a Waterloo decomposition if and only if d is even. 
Cyclic Relative Difference Sets with Classical Parameters
Relative difference sets with n = 2
An Investigation of Group Developed Weighing Matrices
Generalized constructions of Menon-Hadamard difference sets
Structure of group invariant weighing matrices of small weight
Nonlinear functions in abelian groups and relative difference sets
  • A. Pott
  • Computer Science, Mathematics
  • Discret. Appl. Math.
  • 2004
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