The Hadamard conjecture asserts that a Hadamard matrix exists for every positive order divisible by 4. The condition is necessary for every Hadamard matrix of order greater than 2, while many constructions establish existence for particular infinite families of orders.
Hadamard Conjecture
See also
Hadamard Design, Hadamard Matrix, Paley ConstructionExplore with Wolfram|Alpha
References
Hedayat, A. and Wallis, W. D. "Hadamard Matrices and Their Applications." Ann. Stat. 6, 1184-1238, 1978.Cite this as:
Weisstein, Eric W. "Hadamard Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HadamardConjecture.html