Special Arcs in PG(3,13)

Authors

DOI:

https://doi.org/10.23851/mjs.v33i4.1197

Keywords:

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.

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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.

CrossRef

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

CrossRef

Y. Kageyama and T. Maruta, "On the geometric constructions of optimal linear codes", Designs, Codes and Cryptography. 81(3), 2016, pp. 469-480.

CrossRef

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.

CrossRef

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.

CrossRef

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.

CrossRef

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.

CrossRef

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/‎.

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Key Dates

Published

30-12-2022

Issue

Section

Original Article

How to Cite

[1]
S. M. Attook and E. B. . Al-Zangana, “Special Arcs in PG(3,13)”, Al-Mustansiriyah J. Sci., vol. 33, no. 4, pp. 86–91, Dec. 2022, doi: 10.23851/mjs.v33i4.1197.

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