On a class of symmetric designs

Abstract

Non-degenemte quadrics in PG( d, 2), where d is odd and $d ≥ 3$, are used to construct a class of $(2^d+1, 2^d + ε2^(d-1)/2, 2^d-1 + ε2^(d-1)/2)$-designs, where $ε = \pm 1$. The constructed, designs are shown lo be isomorphc to the designs witb these parameters considered by Kantor (1975). The set of values taken by the number of absolute points of a Polarity of these designs is shown to be ${ 0, 2^d, 2^d+1 }$.