Results in Projective Geometry PG(r,23) , r =1,2

In projective plane over a finite field Fq , a conic is the unique complete (q +1) - arc and any arcs on a conic are incomplete arc of degree less than q +1 . These arcs correspond to sets in the projective line over the same field. In this paper, The number of inequivalent incomplete k - arcs; k = 5, 6, ,12 , on the conic in PG(2, 23) PG(1, 23) tetrads. and stabilizer group types are found. Also, the projective line has been splitting into two 12-sets and partitioned into six disjoint