Weighted \((k,n)\)-arcs of Type \((n-q,n)\) and Maximum Size of \((h,m)\)-arcs in \(PG(2,q)\) - Yaseen, Mustafa T.; Ali, Ali Hasan; Shanan, Ibrahim A. (Communications in Mathematics and Applications, 2019)
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 \(PG(2, q)\), 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 \(PG(2, q)\).