4 problems

Jedwab–Pender conjecture. There exists a quaternary Legendre pair of even length $2N$ for every $N\geq 1$.

Let $\ell$ be a positive integer divisible by $5$, and let $(\mathbf{u},\mathbf{v})$ be an LP of length $\ell$. The divisibility-by-five conjecture. One should have … The claim is…

Let an LP (Legendre pair) of length $\ell$ be a pair satisfying the rank-$1$ constrained semidefinite description for the Legendre pair problem. The Legendre-pair existence conject…

Let $ll$ be an odd positive integer with $ll a 0 , (mathrm{mod}; 5)$, and write $ll=5m$. A Legendre pair is a pair $(A,B)$ of sequences of length $ll$, and $mathrm{PSD}A(m)$ an…