Applications geometry of space in PG(3, P)

Abstract

One of the most important applications geometry of space in PG (3, P) over Galois field GF(P), P = 5 is the (k, r)-cap .The aim of this paper is to give a geometric construction of surface complete (k, r)-cap in PG(3, 5). We found that the maximum complete (k, 2)-cap which is called an ovaloid exists in PG (3, 5) when k = 14. Moreover, the complete (k, 3)-cap, (k, 4)-cap and (k, 5)-cap, (k, 6)-cap and we obtain a new example Theorem (2.6).