Hadamard Conjecture

Open Question

Let $n \in \Z$ be a (strictly) positive integer.

Then there exists a $\mathbf A$ be a Hadamard matrix for order $4 n$.

Progress

As of March $2024$, There remain the following multiples of $4$ less than $2000$ for which it is not known whether a Hadamard matrix exists:

$668$, $716$, $892$, $1132$, $1244$, $1388$, $1436$, $1676$, $1772$, $1916$, $1948$, $1964$

Source of Name

This entry was named for Jacques Salomon Hadamard.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Hadamard matrix
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Hadamard matrix
• On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008): A007299