Special Arcs in PG(3,13)
DOI:
https://doi.org/10.23851/mjs.v33i4.1197Keywords:
Arcs, Finite field, Gap, Group action, Projective space.Abstract
In this paper, we constructed new arcs in the three-dimensional projective space over GF(13) of degrees 2, 3, 4, 5, 6, 7, 10, 11, 14, 15, 18, 19, 23, 28, 30, 47, 55, 98 and sizes 2, 4, 5, 7, 10, 14, 17, 20, 28, 34, 35, 68, 70, 85, 119, 140, 170, 238, 340, 476, 595, 1190. These arcs are classified to complete and incomplete arcs. Also, the incomplete arcs are extended to complete arcs.
Metrics
References
J. W. P. Hirschfeld, "Finite projective spaces of three dimensions," New York: Ox-ford Mathematical Monographs, The Clarendon Press, Oxford University Press, 1985.
S. Ball and J.W.P. Hirschfeld, "Bounds on (n,r)-arcs and their application to linear codes", Finite Fields and Their Applications, 11, 2005, pp. 326-336.
J. W. P. Hirschfeld and J.A. Thas," Open problems in finite projective spaces", Finite Fields and Their Applications, 32, 2015, pp. 44-81.
Y. Kageyama and T. Maruta, "On the geometric constructions of optimal linear codes", Designs, Codes and Cryptography. 81(3), 2016, pp. 469-480.
A. Sh. Al-Mukhtar,"Complete arcs and surfaces in three dimensional projective space over Galois filed", PhD. Thesis, University of Technology, Iraq, 2008.
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, 2013, pp. 183-196.
A. A. A. Abdulla and N. Y. Kasm Yahya," Complete arcs and surfaces in three dimensional projective space PG(3,7)", Open Access Library Journal, 7(4), 2020, pp. 1-15.
N. Y. Kasm Yahya, and A.E.M. Sulaimaan," The reverse construction of complete (k,n)-arcs in three dimensional projective space PG(3,4). J. Phys.: Conf. Ser. 2020, pp. 1591 012078.
N. A. M. Al-seraji, A.J. Al-Rikabi, and E.B. Al-Zangana," New arcs in PG(3,8) by Singer group", Al-Mustansiriyah Journal of Science, 33(2), 2022, pp.70-76.
J. Sh. Radhi, and E.B. Al-Zangana," Construction of complete (k;r)-arcs from orbits in PG(3,11)", Al-Mustansiriyah Journal of Science, 33(3), 2022. To appear.
J. W. P. Hirschfeld, "Projective geometries over finite fields. 2nd edn., New York: Ox-ford Mathematical Monographs, The Clarendon Press, Oxford University Press, 1998.
J. A. Gallian, "Contemporary abstract algebra. 9th edn., Cengage Learning, USA, 2017.
The GAP Group," GAP. Reference manual. Version 4.11.1 released on 02 March 2021. [Online]. https://www.gap-system.org/.
Downloads
Published
How to Cite
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.
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.