Description
Given natural numbers $t\leq s\leq n$ and an $n$-dimensional vector space $X$ (over a finite field), a blocking set is a collection of $t$-dimensional subspaces of $X$ such that every $s$-dimensional subspace of $X$ contains a member of the collection. The blocking problem asks for the minimum size and structure of such blocking sets. This problem (together with its applications in coding theory) has been studied by many authors over the past $50$ years. Nevertheless, exact solutions are known only in a few cases including $t=1$, and $(s,t)=(2,1)$ for $n\leq 5$.
In this talk, we develop a general recursive method for constructing (not necessarily minimal) blocking sets by combining constructions in a fixed subspace $K\leq X$ and in the corresponding quotient $X/K$. Using this approach, we improve previously known lower bounds for the blocking problem in the case $(s,t)=(2,1)$ for general $n$.
Joint work with Benedek Kovács, Zoltán Lóránt Nagy.
Blocking planes by lines in $PG(n,q)$. Designs, Codes and Cryptography 93, 4403–4432 (2025). https://doi.org/10.1007/s10623-025-01678-w
https://us06web.zoom.us/j/88170589772?pwd=alKno1wb6whK00eKns7wzgezSDg3vi.1
Meeting ID: 881 7058 9772
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