Arcs in the Finite Projective Space of Dimension Five Over F_2

Emad Bakr  Al-Zangana; Elaf Abdul Satar  Shehab

doi:10.24996/ijs.2026.67.1.24

Authors

Emad Bakr Al-Zangana Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
Elaf Abdul Satar Shehab Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2026.67.1.24

Keywords:

Arc, Complete Arc, Finite field, Finite projective space, Vector space

Abstract

The study of arcs in finite projective spaces involves investigating their cardinality, structure, and relationships with other geometric objects. Different types of arcs can be distinguished based on their properties, such as size and degree. In this paper, the arcs of the finite projective space, PG(5,q),q=2 are studied depending on the orbits that formed from the action of the projective linear group PGL(6,2) on PG(5,2). Each arc is extending by its degree until degree thirty one. Also, for a fixed degree, the size of each arc is extending until to be complete. Finally, the maximum value k for an (k;r)-arc, m_r (5;2) is determined for some r.