Construction of Complete (k;r)-Arcs from Orbits in PG(3,11)

Authors

  • 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.

DOI:

https://doi.org/10.23851/mjs.v33i3.1147

Keywords:

Arc, Complete arc, Companion matrix, Projective space.‎

Abstract

The aim of this research is to partition  into orbits using the subgroups of  which are determined by the nontrivial positive divisors of the order of  . These orbits were also studied from the perspective of arcs by finding complete and incomplete arcs.

Downloads

Download data is not yet available.

References

F.F. Kareem, "The construction of ‎complete (k;n)-arcs in 3-dimensional projective ‎space over Galois field GF(4)," Mustansiriyah. J. ‎Sci. Edu., vol. 1, p. 183196, 2013.

E.B. Al-Zangana, "Splitting of PG(1,27) by sets ‎and orbits, and arcs on the conic," Iraqi J. Sci., vol. 62, no. 6, p. 1979-1985, 2021.

CrossRef

E.B. Al-Zangana, and N.Y. Kasm Yahya, "Subgroups and orbits by companion matrix in ‎three dimensional projective space," Baghdad ‎Science Journal, vol. 19, no. 4, p. 0805, 2022.

CrossRef

N.A. Al-Seraji, N, E.A. Alnussairy, and Z.S. Jafar, "The group action on the finite projective ‎planes on order 53,61,64," Journal of discrete ‎Mathematical Sciences and Cryptography, vol. 23, no. 8, pp. 1573-1582, 2020.

CrossRef

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

CrossRef

J.W.P. Hirschfeld, Finite projective ‎spaces of three dimensions.: Oxford University ‎Press, 1985.

A.Sh. Al-Mukhtar, Complete arcs and ‎surfaces in three dimensional projective ‎space over Galois filed. PhD. Thesis: University of ‎Technology, Iraq, 2008.

A.Sh. Al-Mukhtar, "On projective 3-‎space over Galois field," Ibn Al-Haitham Journal For ‎Pure and Applied Science, vol. 25, no. 1, pp. 259-265, 2012.

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

The GAP Group, "Reference manual", GAP, 2022.

Online

J.W.P. Hirschfelda, and J.A. Thas, "Open problems in finite projective spaces," Finite Fields and Their Applications, vol. 32, pp. 44-81, 2015.

CrossRef

N.Y.‎ Kasm Yahya, "Applications geometry of ‎space in PG(3,p)," J. Interdiscip. Math., vol. 25, no. 2, pp. 285-297, 2022.

CrossRef

A.A.A. Abdulla, and N.Y. Kasm Yahya, "Application of ‎algebraic geometry in three dimensional ‎projective space PG(3,7)," J. phys. Conf. Ser., vol. 1591, no. 1, p. 012077, 2020 ‎‎‎.

CrossRef

Downloads

Key Dates

Published

25-09-2022

Issue

Section

Original Article

How to Cite

[1]
J. S. Radhi and E. B. Al-Zangana, “Construction of Complete (k;r)-Arcs from Orbits in PG(3,11)”, Al-Mustansiriyah Journal of Science, vol. 33, no. 3, pp. 48–53, Sep. 2022, doi: 10.23851/mjs.v33i3.1147.

Similar Articles

1-10 of 77

You may also start an advanced similarity search for this article.