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New sizes of complete (k, 4)-arcs in PG(2,17)

Authors

  • Zainab Shehab Hamed Department of Mathematics, College of Science, Mustansiriyah University, Iraq

DOI:

https://doi.org/10.21123/bsj.2022.6820

Keywords:

Complete arc, Group of complete (k,n)-arc, Inequivalent secant distribution, PG(2,17), PG(2,13)

Abstract

              In this paper, the packing problem for complete (  4)-arcs in  is partially solved. The minimum and the maximum sizes of complete (  4)-arcs in  are obtained. The idea that has been used to do this classification is based on using the algorithm introduced in Section 3 in this paper. Also, this paper establishes the connection between the projective geometry in terms of a complete ( , 4)-arc in  and the algebraic characteristics of a plane quartic curve over the field  represented by the number of its rational points and inflexion points. In addition, some sizes of complete (  6)-arcs in the projective plane of order thirteen are established, namely for  = 53, 54, 55, 56.

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References

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