The Reverse construction of complete (k, n)- arcs in three-dimensional projective space PG(3,4)

Abstract

In this work, the complete (k, n) arcs in PG(3,4) over Galois field GF(4) can be created by removing some points from the complete arcs of degree m, where m = n + 1, 3 n q2 + q is used. In addition, where k ≤ 85, we geometrically prove that the minimum complete (k, n)–arc in PG(3,4) is (5,3)-arc. A(k, n)–arcs is a set of k points no n+1 of which collinear. A(k, n)–arcs is complete unless it is embedded in an arc (k+l,n).