The College of Science, Department of Mathematics, has discussed a master's thesis entitled "Second- and Third-Order Gaps in Seventh-Order Projective Spaces" by postgraduate student Mohammed Sami Awad. The thesis aims to study gaps of types (ν,2) and (ν,3) in this space, identifying potential new types of gaps. Since the size of the largest of these gaps is unknown in PG(3,7) and their number is much greater in seventh-order projective space than in fifth-order projective space, this study provides a large number of such gaps for study. One of the main applications of these gaps is the study of fourth-dimensional projective linear codes, which are important in cryptography theory.
