Extension of Size and Degree of (k,r)-Caps in PG(3,13)

Abstract

The aim of this work is an extension of the -caps ( is the order, is the degree), where , in the three projective space of dimension over the Galois field of order thirteen, . The extensions have been done on the caps founded by action subgroups of projective general linear of order four over the finite field of order thirteen on . The main condition for the completion of the expansion process on the degree of caps is (number of points on the line in ) and the size of the cap is points with a zero index zero, as it becomes complete when it is equal to zero. In this paper, we present fifteen caps (completes and incompletes) in of degrees 2,3,4,7 are extended in size until they reach 14, which are then complete caps, and then the -distribution are computed for each new cap.

Keywords

• Cap, Complete cap, Finite projective space, Group action.