4 problems

Existence conjecture. Skew-symmetric conference matrices exist for every order divisible by four.

Generalized circulant Hadamard conjecture. The relation

Let $n$ be an integer with … Let $f_k(n)$ be the maximum determinant of $n\times n$ skew matrices with diagonal entries $0$ and off-diagonal entries in $\{-1,1\}$, and let $g_k(n)$…

Let $p$ be a prime, and let ${\mathbb C}$ be a code of length $p+1$ constructed from a generator matrix that is a conference matrix. Conference-matrix MDS conjecture. The code…