All Questions

What is the smallest possible size of a set of points in $\mathbb{F}_q^3$ which intersects (blocks) every line? Clearly the union of three affine hyperplanes that intersect in a singleton, say $x = 0,...

$\newcommand{\F}{\mathbb F}$ A subset $P$ of the affine plane $\F_p^2$ is said to determine a direction if there is a line in this direction containing at least two points of $P$. A set of size $|P|&...

By a classical result of Singer (1938), for a prime number $p$ the cyclic group $C_n$ of order $n=1+p+p^2$ contains a subset $D$ of cardinality $|D|=1+p$ such that $DD^{-1}=C_n$. Such set $D$ is ...

Let's define $k$-blocking set in affine space $AG(n,q)$ a set that meets every coset (translate of subspace) of dimension $k$. I have seen a lot work related to minimal $(n-1)$-blockings set. ...

Given a prime power $q$, I would like to enumerate (preferably up to isomorphism*) all the permutation polynomials $f(x)$ on $K = GF(q^3)$ satisfying the following conditions: $f(ax) = af(x)$ for all ...