Neutrosophic and Information Fusion

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Volume 3 , Issue 2 , PP: 1-8, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

Finding the complete List of Different K-Brackets for the Projective Plane PG (2, 8)

Khaled Moaz 1 *

  • 1 University of Mosul, department of computer science and mathematics, Mosul, Iraq - (Khaledmoaz_m13@gmail.com)
  • Doi: https://doi.org/10.54216/NIF.030201

    Received: November 25, 2023 Accepted: March 20, 2024
    Abstract

    A k-arc in a plane PG (2, q) is a set of k point such that every line in the plane intersect it in at most two points and there is a line intersect it in exactly two points. A k-arc is complete if there is no k+1-arc containing it. This thesis is concerned with studies a k-arcs, k=4, 5,…., 10 and classification of protectively distinct k-arcs and distinct arcs under collineation. We prove by using computer program that the only complete k-arcs is for, k= 6, 10.

    Keywords :

    k-bracket , Projection , Projective plane , k-arc

    References

    [1]          Aziz, S.M., (2001), "On Lower Bound for Complete (k,n)-arc in PG(2,q)", M.Sc. Thesis , University of Mosul .

    [2]          Chao,J.M. and Kaneta. H., (2001), "Classial arcs in PG(r,q) for 23≤q≤29" Discrete Mathematics 226,p.p.377-385

    [3]          Coolsaet, K. and Sticker, H., "A full classification of complete k-arcs in PG(2,23) and PG(2,25)", Journal of Combinatorial Designs

    [4]          Coolsaet, K. and Sticker, H., (2009),"A full classification of complete k-arcs in PG(2,27)"

    [5]          Hasan, F. A. (2004), “On some complete arcs and Algebraic Curves,” M. SC. Thesis, University of Mosul.

    [6]          Hirschfeld, J.W.P., (1979), "Projective Geometrics over Finite Fields", Oxford University Press, Oxford.

    [7]          Hirschfeld, J. W. P. and Storme, L., (2001), "The packing problem in statistics, coding theory and finite projective spaces: Update 2001", Submitted.

    [8]          Thomas, A.D. and Wood, G.V., (1980), "Group Tables", Shiva Publishing Ltd.

    [9]          Yasin, A.L., (1986), "Cubic arcs in the projective plane of order eight", Ph.D. Thesis, University of Sussex.

    [10]       Younis, H., (1989), "Classification of k-arcs in the projectivety plane PG(2,16)", M.Sc. Thesis, University of Mosul.

    Cite This Article As :
    Moaz, Khaled. Finding the complete List of Different K-Brackets for the Projective Plane PG (2, 8). Neutrosophic and Information Fusion, vol. , no. , 2024, pp. 1-8. DOI: https://doi.org/10.54216/NIF.030201
    Moaz, K. (2024). Finding the complete List of Different K-Brackets for the Projective Plane PG (2, 8). Neutrosophic and Information Fusion, (), 1-8. DOI: https://doi.org/10.54216/NIF.030201
    Moaz, Khaled. Finding the complete List of Different K-Brackets for the Projective Plane PG (2, 8). Neutrosophic and Information Fusion , no. (2024): 1-8. DOI: https://doi.org/10.54216/NIF.030201
    Moaz, K. (2024) . Finding the complete List of Different K-Brackets for the Projective Plane PG (2, 8). Neutrosophic and Information Fusion , () , 1-8 . DOI: https://doi.org/10.54216/NIF.030201
    Moaz K. [2024]. Finding the complete List of Different K-Brackets for the Projective Plane PG (2, 8). Neutrosophic and Information Fusion. (): 1-8. DOI: https://doi.org/10.54216/NIF.030201
    Moaz, K. "Finding the complete List of Different K-Brackets for the Projective Plane PG (2, 8)," Neutrosophic and Information Fusion, vol. , no. , pp. 1-8, 2024. DOI: https://doi.org/10.54216/NIF.030201