A remark on blocking sets of almost R�dei type

Abstract

In [1] it is shown that ifB is a minimum size blocking set in PG(2,p),p prime, such that there is a lineL meetingB in at least s|B|−p−p+45/20 points, thenB/L consists ofp, p + 1 orp + 2 points. It has been known for a long time that for anyp > 2 there is a unique example with ¦B/L¦= p [2]. In [3] the authors prove that ¦B/L¦ =p + 1 can only occur whenp ≤7. Here we show that if¦B/L¦= p+2, thenp = 3, 5 or 7, and all examples are classical ones. Besides combinatorial arguments we use polynomials over finite fields and a formula that generalizes the Newton formulae relating power sums and elementary symmetric polynomials.