Projective geometric codes (Q1865375)

In the very nice paper under review the authors determine the words of minimum weight in the code of the incidence system of \(s\)- versus \(t\)-flats in a finite projective space \(\text{PG}(n,q)\). For \(0\leq s<t<n\), let \(\Delta_{s,t}(n,q)\) denote the incidence system whose points and blocks are the \(s\)- and \(t\)-flats in \(\text{PG}(n,q)\), and the incidence is the set-theoretic inclusion. Let \(C_{s,t}(n,q)\) denote the \(p\)-ary code of \(\Delta_{s,t}(n,q)\). The main result states that the minimum weight words of \(C_{s,t}(n,q)\) are the scalar multiples of the blocks of \(\Delta_{s,t}(n,q)\).