Weighted \((k,n)\)-arcs of Type \((n-q,n)\) and Maximum Size of \((h,m)\)-arcs in \(\mathrm{PG}(2,q)\)


  • Mustafa T. Yaseen Department of Business Administration, Shatt Al-Arab University College, Basrah
  • Ali Hasan Ali Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah
  • Ibrahim A. Shanan Business Management Techniques Department, Management Technical College, Southern Technical University, Basrah




\((k, n)\)-arcs, Weighted \((k, n)\)-arc, \(\mathrm{PG}(2, q)\), \text{prime})\), Projective plane, Galois plane, Algebraic geometry


In this paper, we introduce a generalized weighted \((k, n)\)-arc of two types in the projective plane of order \(q\), where \(q\) is an odd prime number. The sided result of this work is finding the largest size of a complete \((h, m)\)-arcs in \(\mathrm{PG}(2, q)\), where \(h\) represents a point of weight zero of a weighted \((k, n)\)-arc. Also, we prove that a \(\big(\frac{q(q-1)}{2}+1, \frac{q+1}{2}\big)\)-arc is a maximal arc in \(\mathrm{PG}(2, q)\).


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How to Cite

Yaseen, M. T., Ali, A. H., & Shanan, I. A. (2019). Weighted \((k,n)\)-arcs of Type \((n-q,n)\) and Maximum Size of \((h,m)\)-arcs in \(\mathrm{PG}(2,q)\). Communications in Mathematics and Applications, 10(3), 361–368. https://doi.org/10.26713/cma.v10i3.1275



Research Article