5 problems

Craigen–Holzmann–Kharaghani conjecture. Complex Golay pairs do not exist in length $23$.

Let $(A,B)$ be the $(v/2)$-decomposition of a periodic Golay pair $\operatorname{PG}(v)$ with row sums $a$ and $b$. Equivalence is taken in the sense used for these decompositions.…

The nonexistence conjecture for length 23. The integer $23$ is not a complex Golay number; equivalently, no complex Golay pair of length $23$ exists.

A Hadamard matrix of 2N-type is a Hadamard matrix of order $2v$ of the block form … where $A$ and $B$ are negacyclic blocks. 2N-type existence conjecture. For each even integer…

A negaperiodic Golay pair (NG-pair) is a pair of binary sequences satisfying the negaperiodic Golay complementary condition. Ito's conjecture. Ito's conjecture about Hadamard matri…