Hadamard matrices modulo p and small modular Hadamard matrices Kuperberg, Vivian Zieve modular hadamard matrices modular symmetric designs 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. Wiley 2016 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22202 Kuperberg VZ. Hadamard matrices modulo p and small modular Hadamard matrices. <i>Journal of Combinatorial Designs</i>. 2016;24(9):393-405. doi:<a href="https://doi.org/10.1002/jcd.21522">10.1002/jcd.21522</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1002/jcd.21522 info:eu-repo/semantics/altIdentifier/issn/1063-8539 info:eu-repo/semantics/altIdentifier/e-issn/1520-6610 info:eu-repo/semantics/altIdentifier/arxiv/1409.0148 info:eu-repo/semantics/openAccess