Small minimal blocking sets in \(\text{PG}(2,q^3)\)
A blocking set \(B\) in PG\((2,q)\), \(q=p^n\), \(p\) prime, is called small if \(|B|<3(q+1)/2\). The exponent of \(B\) is the greatest integer \(e\) such that every line intersects \(B\) in 1 (mod \(p^e\)) points. The authors classify all minimal blocking sets in PG\((2,q^3)\), \(q=p^h\), \(p\geq 7\), with exponent \(e\geq h\), extending the results by \textit{O. Polverino} [Discrete Math. 208-209, 469-476 (1999; Zbl 0941.51008) and Des.\ Codes Cryprography 20, 319-324 (2000; Zbl 0969.51016)]. Such classification includes all minimal blocking sets of size at most \(q^3+q^2+q+1\).
scientific article; zbMATH DE number 1740671