An easier method for finding all types of (k,n;{1,2})-arcs in PG(2,q) , q odd

J. Mohammed, Makbola

	An easier method for finding all types of (k,n;{1,2})-arcs in PG(2,q) , q odd
Tikrit Journal of Pure Science
Article 1, Volume 19, Issue 5, 2014, Pages 128-134
Author
Makbola J. Mohammed
Abstract
Abstract: In this work, we study the (k,n;f)-arcs in a projective plane PG(2,q), q=ph , p is any positive prime number greater than 2 , and h is any positive integer number. This research presents a new and fast method to determine these arcs, by using this method we can prove that the number of (k,n;{1,2})-arcs in PG(2,q), q=ph are (q+2). Then finding for example all (k,n;{1,2})-arcs in PG(2,17) whose numbers are (19). Only two types of these arcs are known in [6], also finding all (k,n;{1,2})- arcs in the two projective planes PG(2,23) and PG(2,25) which has been not researched until now, to enable finding in general all arcs in PG(2,q), q=ph , by using an easier equations and in a short time. Bearing in mind that the previous approach was able only in limited manner to specify a limited number of those arcs in the projective plane PG (2,19), no other study exists for those arcs of q >19 values

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