The College of Science in the Department of Mathematics discussed a seminar entitled the Caps of Degrees 2 and 3 in Projective Space of Order Seven for postgraduate student Mohammed S. Awad. This seminar focuses on the study of (n,2)-caps and (n,3)-caps in the projective space of order seven. The motivation for our work in this space is to determine if there are new types of (n,2)-caps and (n,3)-caps. Also, the size of the largest (n,2)-caps and (n,3)-caps is not known in PG(3,7). Moreover, the number of (n,2)-caps and (n,3)-caps is significantly higher in the projective space of order seven than it is in the projective plane of order five, giving a large number of such (n,2)-caps and (n,3)-caps for study. As one main application of (n,2)-caps and (n,3)-caps is to the study of projective linear codes of dimension 4, which play an important role in coding theory.
