Title of article :
Classification and Construction of (k,3)-Arcs on Projective Plane Over Galois Field GF(9)
Author/Authors :
Ahmad, Adil M. University of Baghdad - College of Education for Pure Science (Ibn AL-Haitham) - Department of Mathematics, Iraq , Al-Mukhtar, Amaal SH. University of Baghdad - College of Education for Pure Science (Ibn AL-Haitham) - Department of Mathematics, Iraq , Kareem, Fatima. F. University of Baghdad - College of Education for Pure Science (Ibn AL-Haitham) - Department of Mathematics, Iraq
Abstract :
In this work, we construct and classify the projectively distinct (k,3)-arcs in PG(2,9), where k ≥ 5, and prove that the complete (k,3)-arcs do not exist, where 5 ≤ k ≤ 13. We found that the maximum complete (k,3)-arc in PG(2,q) is the (16,3)-arc and the minimum complete (k,3)-arc in PG(2,q) is the (14,3)-arc. Moreover, we found the complete (k,3)-arcs between them.
Keywords :
arcs , secant , Projective plane , Galois Field
Journal title :
Ibn Alhaitham Journal For Pure and Applied Science
Journal title :
Ibn Alhaitham Journal For Pure and Applied Science
