New Arcs in PG(3,8) by Singer Group
Keywords:Arc, Galois field, Projective space, Singer group.
In this paper, studied the types of (k, r)-arcs were constructed by action of groups on the three-dimensional projective space over the Galois field of order eight. Also, determined if they form complete arcs or not.
J.W.P. Hirschfeld. Finite Projective spaces of three dimensions. New York: Ox-ford Mathematical Monographs, The Clarendon Press, Oxford University Press, 1985. ISBN-13 : 978-0198535362.
J.W.P. Hirschfeld. Projective geometries over finite fields. 2nd edn., New York: Ox-ford Mathematical Monographs, The Clarendon Press, Oxford University Press, 1998. ISBN-13: 978-0198502951.
J.W.P. Hirschfeld and J.A. Thas. Open problems in finite projective spaces. Finite Fields Appl., 32, pp. 44-81, 2015. doi.org/10.1016/j.ffa.2014.10.006.
N.A.M. Al-Seraji, E.A. Al-Nussairy and Z.S. Jafar. The group action on the finite projective planes of orders 53, 61, 64. Journal of Discrete Mathematical Sciences and Cryptography, 23(8), pp. 1573-1582, 2020. doi.org/10.1080/09720529.2020.1773020
N.A.M. Al-Seraji, A. Bakheet and Z.S. Jafar. Study of orbits on the finite projective plane. Journal of Interdisciplinary Mathematics, 23(6), pp. 1187-1195, 2020.
N.A.M. Al-Seraji and R.A.B. Al-Ogali. The group action on a projective plane over finite field of order sixteen. Iraqi Journal of Science (IJS), 58(3), 2017.
E.B. Al-Zangana and S. A. Joudah. Action of groups on the projective plane over the field GF(41). J. Phys.: Conf. Ser. 1003, 012059, 2018.
E.B. Al-Zangana. Splitting of PG(1,27) by sets and orbits, and arcs on the conic. Iraqi Journal of Science (IJS), 62(6), 2021.
E.B. Al-Zangana and N.Y. Kasm Yahya. Subgroups and orbits by companion matrix in three dimensional projective space. Baghdad Sci. J, 2021. To appear.
N.A.M. Al-Seraji, A.J. Al-Rikabi and E.B. Al-Zangana . Caps by Groups Action on the PG(3,8). Iraqi Journal of Science (IJS), 63(4), 2022. To appear.
N.A.M. Al-Seraji, A.J. Al-Rikabi and E.B. Al-Zangana. Represent the space PG(3,8) by subspaces and subgeometries. Sixth National Scientific/Third International Conference at College of Education for Pure Sciences/Kerbala University, Iraq, AIP Conference Proceedings, 2021. To appear.
A. SH. Al-Mukhtar. Complete arcs and surfaces in three dimensional projective space over Galois field. Ph.D. Thesis, University of Technology, Baghdad, Iraq, 2008.
A.A. Abdulla and N.Y. Kasm Yahya. Application of algebraic geometry in three dimensional projective space PG (3,7). J. Phys.: Conf. Ser. 1591, 2020.
F.F. Kareem. The construction of complete (k;n)-arcs in 3-dimensional projective space over Galois field GF(4). Mustansiriyah Journal for Sciences and Education, 1, pp. 183-196, 2013.
M.G. Oxenham. On n-covers of PG(3,q) and related structures. PhD. Thesis, University of Adelaide, Australia, 1991.
How to Cite
Copyright (c) 2022 Al-Mustansiriyah Journal of Science
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Articles accepted for publication in Al-Mustansiriyah Journal of Science (MJS) are protected under the Creative Commons Attribution 4.0 International License (CC BY-NC). Authors of accepted articles are requested to sign a copyright release form prior to their article being published. All authors must agree to the submission, sign copyright release forms, and agree to be included in any correspondence between MJS and the authors before submitting a work to MJS. For personal or educational use, permission is given without charge to print or create digital copies of all or portions of a MJS article. However, copies must not be produced or distributed for monetary gain. It is necessary to respect the copyright of any parts of this work that are not owned by MJS.