3 problems

Existence conjecture. A Steiner quadruple system of order $v$ with locality two and skip cost zero exists for all admissible parameters, namely all $v\geq 4$ satisfying $v\equiv 2$…

Let $f(x)$ and $g(x)$ be irreducible polynomials of degree $k$ and exponent $e$, and suppose that $2k=nm$, where $n>1$ and $m>1$, and $e=rt$ with $\operatorname{gcd}(r,t)=1$. Foldi…

Let $s>2$, and consider the PIR array codes produced by the B-E Construction. B-E optimality conjecture. These PIR array codes have optimal rate. The preceding discussion is based…