@article{22202,
  abstract     = {We use modular symmetric designs to study the existence of Hadamard matrices modulo certain primes. We solve the 7-modular and 11-modular versions of the Hadamard conjecture for all but a finite number of cases. In doing so, we state a conjectural sufficient condition for the existence of a p-modular Hadamard matrix for all but finitely many cases. When 2 is a primitive root of a prime p, we conditionally solve this conjecture and therefore the p-modular version of the Hadamard conjecture for all but finitely many cases when p ≡ 3(mod 4), and prove a weaker result for p ≡ 1 (mod 4). Finally, we look at constraints on the existence of m-modular Hadamard matrices when the size of the matrix is small compared to m.},
  author       = {Kuperberg, Vivian Zieve},
  issn         = {1520-6610},
  journal      = {Journal of Combinatorial Designs},
  keywords     = {modular hadamard matrices, modular symmetric designs},
  number       = {9},
  pages        = {393--405},
  publisher    = {Wiley},
  title        = {{Hadamard matrices modulo p and small modular Hadamard matrices}},
  doi          = {10.1002/jcd.21522},
  volume       = {24},
  year         = {2016},
}