Hadamard Matrices Modulo p and Small Modular Hadamard Matrices |
| |
Authors: | Vivian Kuperberg |
| |
Institution: | Cornell University, Math Department, Ithaca, New York, USA |
| |
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 , and prove a weaker result for . Finally, we look at constraints on the existence of m‐modular Hadamard matrices when the size of the matrix is small compared to m. |
| |
Keywords: | modular hadamard matrices modular symmetric designs |
|
|