Classification and Construction of (k,3)-Arcs on Projective Plane Over Galois Field GF(7)

Authors

  • Adil M. Ahmad
  • Aamal SH. Al-Mukhtar
  • Mahmood S. Faiyadh

Keywords:

Arcs,Projective plane, Galois field

Abstract

  The purpose of this work is to study the classification and construction of (k,3)-arcs in the projective plane PG(2,7). We found that there are two (5,3)-arcs, four (6,3)-arcs, six (7,3)arcs, six (8,3)-arcs, seven (9,3)-arcs, six (10,3)-arcs and six (11,3)-arcs.         All of these arcs are incomplete.         The number of distinct (12,3)-arcs are six, two of them are complete.         There are four distinct (13,3)-arcs, two of them are complete and one (14,3)-arc which is incomplete.         There exists one complete (15,3)-arc.
 

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Published

30-Apr-2017

Issue

Section

Mathematics

Publication Dates