Covers and blocking sets of classical generalized quadrangles

This article discusses two problems on classical generalized quadrangles. It is known that the generalized quadrangle Q(4,q) arising from the parabolic quadric in PG(4,q) has a spread if and only if q is even. Hence, for q odd, the problem arises of the cardinality of the smallest set of lines of Q(4,q) covering all points of Q(4,q). We show in this paper that this set of lines must contain more than q2+1+(q−1)/3 lines. We also show that Q(4,q), q even, does not contain minimal covers of sizes q2+1+r when q⩾32 and 0