From Incomplete to Complete Caps: A Study in PG(3,17)

Section: Research Article
Issue
Vol. 35 No. 4 (2026): Volume 35, Issue 4
Pages
116-126

Abstract

This paper investigated the complete caps of different degrees in the finite three-dimensional projective space on the finite field of order seventeen, . These caps were constructed from thirty-four caps obtained by the right action of thirty-four cyclic subgroups, from the cyclic group generated by the companion matrix, on the projective space. These caps are classified into complete and incomplete caps, and then an extension has been done with respect to the degree and size. The maximum size of caps has been studied amongst all the obtained complete caps. Also, we found the lines that partition the space , whose number was 290 lines.

Keywords:

Action of group, finite field, finite projective space, cap.

References

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Authors

Tabark Hassan Najim

Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq

Emad Bakr Al-Zangana

Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq

Identifiers

DOI: 10.33899/ytpy3506

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[1]
“From Incomplete to Complete Caps: A Study in PG(3,17)”, JES, vol. 35, no. 4, pp. 116–126, Oct. 2026, doi: 10.33899/ytpy3506.
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How to Cite

[1]
“From Incomplete to Complete Caps: A Study in PG(3,17)”, JES, vol. 35, no. 4, pp. 116–126, Oct. 2026, doi: 10.33899/ytpy3506.