Renitent lines

There are many examples for point sets in finite geometry which behave "almost regularly"in some (well-defined) sense, for in-stance they have "almost regular"line-intersection numbers. In this paper we investigate point sets of a desarguesian affine plane, for which there exist some (sometimes: many) parallel classes of lines, such that almost all lines of one parallel class intersect our set in the same number of points (possibly mod p, the characteristic). The lines with exceptional intersection numbers are called renitent, and we prove results on the (regular) behavior of these renitent lines. As a consequence of our results, we also prove geometric properties of codewords of the Fp-linear code generated by characteristic vectors of lines of PG(2, q)