Construction of Complete (k;r)-Arcs from Orbits in PG(3,11)
DOI:
https://doi.org/10.23851/mjs.v33i3.1147Keywords:
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
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.
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.
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.
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.
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.
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.
N.Y. Kasm Yahya, "Applications geometry of space in PG(3,p)," J. Interdiscip. Math., vol. 25, no. 2, pp. 285-297, 2022.
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 .
Downloads
Key Dates
Published
Issue
Section
License
Copyright (c) 2022 Al-Mustansiriyah Journal of Science

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
(Starting May 5, 2024) Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution (CC-BY) 4.0 License that allows others to share the work with an acknowledgement of the work’s authorship and initial publication in this journal.