Open AccessThe Reverse construction of complete (k, n)- arcs in three-dimensional projective space PG(3,4)
Author(s) -
Aidan Essa Mustafa Sulaimaan,
Nada Yassen Kasm Yahya
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1591/1/012078
Subject(s) - arc (geometry) , mathematics , combinatorics , projective space , set (abstract data type) , field (mathematics) , space (punctuation) , discrete mathematics , geometry , projective test , pure mathematics , computer science , programming language , operating system
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).