New Arcs in PG(3,8) by Singer Group

Authors

  • Najm Abdulzahra Al-seraji Department of Mathematics, College of Science, Mustansiriyah University.
  • Abeer Jabbar Al-Rikabi Department of Mathematics , College of Basic Education, Mustansiriyah University. https://orcid.org/0000-0002-4446-9447
  • Emad B. Al-Zangana Department of Mathematics, College of Science, Mustansiriyah University.

DOI:

https://doi.org/10.23851/mjs.v33i2.1128

Keywords:

Arc, Galois field, Projective space, Singer group.

Abstract

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.

References

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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.

CrossRef

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

CrossRef

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.

CrossRef

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.

CrossRef

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. ‎

CrossRef

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.

CrossRef

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.

CrossRef

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.

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Published

2022-06-26

How to Cite

[1]
N. A. . Al-seraji, A. J. Al-Rikabi, and E. B. . Al-Zangana, “New Arcs in PG(3,8) by Singer Group”, MJS, vol. 33, no. 2, pp. 70–76, Jun. 2022.

Issue

Section

Mathematics