Special Arcs in PG(3,13)

Abstract

In this paper, we constructed new arcs in the three-dimensional projective space over GF(13) of degrees 2, 3, 4, 5, 6, 7, 10, 11, 14, 15, 18, 19, 23, 28, 30, 47, 55, 98 and sizes 2, 4, 5, 7, 10, 14, 17, 20, 28, 34, 35, 68, 70, 85, 119, 140, 170, 238, 340, 476, 595, 1190. These arcs are classified to complete and incomplete arcs. Also, the incomplete arcs are extended to complete arcs.

Keywords

• Arcs, Finite field, Gap, Group action, Projective space.