5 problems

Let $q=2^n$, let $x^s$ be an o-monomial over $\operatorname{GF}(2^n)$, and define … Here an o-monomial is a monomial o-polynomial. O-monomial 3-design conjecture. If $x^s$ is any o…

Let $m\geq 5$ be odd, set $q=2^m$, and let $\hat{\mathbb{D}}(f,k)=({\mathrm{GF}}(q),\hat{\mathcal{B}}_k)$ be the extended construction, with $k=q/2$. Define the listed o-polynomial…

Let $m\geq 5$ be odd, set $q=2^m$, and let $f$ be an o-polynomial over ${\mathrm{GF}}(q)$. Let $\hat{\mathcal{B}}_{(f,q/2)}$ be the distinct blocks in the extended construction. Th…

Let $q=2^m$, let $x^e$ be an o-monomial over ${\mathrm{GF}}(q)$, and let $J_e$ be the associated subset used in the design construction. Write ${\mathrm{AG}}_1({\mathrm{GF}}(q))$ f…

Let $q=2^m$, and let $f$ be an o-polynomial over ${\mathrm{GF}}(q)$. For $a\in {\mathrm{GF}}(q)^*$ and $h$ satisfying $1\leq h<m$ and $\gcd(h,m)=1$, exclude the translation o-monom…