Minimal blocking sets of size \(2p-2\) and \(2p-3\) in \(PG(2, p)\), \(p\) prime and \(p > 5\) (Q2482311)

A subset \(B\) of the 2-dimensional projective plane \(PG(2,q)\) is said to be a \textit{blocking set} if it meets every line but contains no line completely, that is, \(1\leq \left| B\cap l\right| \leq q\) for every line in \(PG(2,q)\). A blocking set \(B\) is \textit{minimal} if \(B\backslash\left\{P\right\}\) is not a blocking set for every \(P\) in \(B\). Finally, a blocking set is of \textit{Rédei type} with respect to a line \(l\) if \(\left| B\cap l\right| =\left| B\right| -q\). In this paper the author presents a new general construction of blocking sets of Rédei type in \(PG(2,p)\) when \(p\) is a prime, \(p>5\), and \(p\equiv 1\) (mod 4) or \(p\equiv 3\) (mod 4). The sizes of these blocking sets are \(2p-3\) and \(2p-2\), respectively.