Extension of Cap by Size and Degree in the Space PG(3,11)‎

Article Sidebar

pdf
Published: Apr 20, 2023
DOI: https://doi.org/10.30526/36.2.3025
Keywords:
Cap, Complete (Incomplete) cap, Companion matrix, Projective space, τ_i- distribution, c_i-distribution.

Main Article Content

Jabbar Sharif Radhi
Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq.
Emad Bakr Al-Zangana
Department of Mathematics, College of Science,Mustansiriyah University, Baghdad, Iraq.

Abstract

A cap of size  and degree  in a projective space, (briefly; (k,r)-cap) is a set of  points with the property that each line in the space meet it in at most  points. The aim of this research is to extend the size and degree of complete caps and incomplete caps, (k, r)-caps of degree r<12 in the finite projective space of dimension three over the finite field of order eleven, which already exist and founded by the action of subgroups of the general linear group over the finite field of order eleven and degree four, to (k+i,r+1) -complete caps. These caps have been classified by giving the t_i-distribution and -distribution. The Gap programming has been used to execute the designed algorithms and computations.

Article Details

How to Cite
Extension of Cap by Size and Degree in the Space PG(3,11)‎. (2023). Ibn AL-Haitham Journal For Pure and Applied Sciences, 36(2), 375-382. https://doi.org/10.30526/36.2.3025
Issue
Vol. 36 No. 2 (2023)
Section
Mathematics
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

licenseTerms

How to Cite

Extension of Cap by Size and Degree in the Space PG(3,11)‎. (2023). Ibn AL-Haitham Journal For Pure and Applied Sciences, 36(2), 375-382. https://doi.org/10.30526/36.2.3025
Crossref
Scopus
Google Scholar
Europe PMC

Publication Dates

References

Hirschfeld, J.W.P, Finite projective spaces of three dimensions, New York: Ox-ford Mathematical Monographs, The Clarendon Press, Oxford University Press, 1985.

Hirschfeld, J.W.P, Projective geometries over finite fields. 2nd edn., New York: Ox-ford Mathematical Monographs, The Clarendon Press, Oxford University Press, 1998.

Radhi, J.Sh.; Al-Zangana, E.B.. Complete (k,r)-caps from orbits in PG(3,11)‎. Iraqi Journal of Science (IJS), To appear. 2022, 64(1).

Al-seraji, N.A.; Al-Rikabi, A.J.; Al-Zangana, E.B.. Caps by groups action on the PG(3,8). Iraqi Journal of Science (IJS), 2022, 63(4),1755-1764.

Al-Zangana, E.B.;Kasm Yahya, N.Y.. Subgroups and orbits by companion matrix in three dimensional projective ‎space. Baghdad Sci. J., 2022, 19(4), 805-810.

Al-Zangana, E.B.; Joudah, S.A.. Action of group ‎on the projective plane over field GF(41). J. phys. ‎Conf. Ser., 2018, 1033(1):012059.

Al-Seraji, N.A.; Alnussairy, E.A.; Jafar, Z.S. The group action on the finite projective ‎planes on order 53,61,64. Journal of discrete ‎Mathematical Sciences and Cryptography, 2020, 23(8), 1573-1582.

The GAP Group. GAP. Reference manual. Version 4.11.1 released on ‎‎02 March 2021. [Online]. https://www.gap-system.org.