Use Algebra of Group Action to Find Special Types of Caps in PG(3,13)

Saja Makki Attook; Emad Bakr Al-Zangana

doi:10.24996/ijs.2023.64.8.31

Authors

Saja Makki Attook Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq https://orcid.org/0000-0003-0195-2188
Emad Bakr Al-Zangana Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2023.64.8.31

Keywords:

Cap, Finite projective space, Finite field, Gap, Group action

Abstract

Group action on the projective space PG(3,q) is a method which can be used to construct some geometric objects for example cap. We constructed new caps in PG(3,13) of degrees 2, 3, 4, 7,14 and sizes 2, 4, 5, 7, 10, 14, 17, 20, 28, 34, 35, 68, 70, 85, 119, 140, 170, 238, 340, 476, 595, 1190. Then the incomplete caps are extended to complete caps.