Classification of some arcs of type (m,n) in PG(2,19) - Makbola. Mohamed; Ban. Qassim; Layla Jasim (College of Education for Pure Sciences, 2009)
Abstract: This paper conclude the study of the weights of points and lines of (k,n)-arcs from until , since the number of points and lines of this plane is very large, so we divide this search in to three parts. The first part contained the existence of these arcs from to and we show that when the (210,39;f)-arc of type (20,39) exist and all the other cases from to does not exist. In the second part we studied these arcs from to and we saw that there are two types of these arcs when and which are respectively (39,21;f)- arc of type (2,21) and (20,20;f)- arc of type (1,20), then proved the theorem of these special cases are given. Finally in the last step we prove that (k,n;f)- arc of type (n-19,n) does not exist in PG(2,19) for all values of from 362 to 381.