Abstract
In this paper, the packing problem for complete ( 4)-arcs in is partially solved. The minimum and the maximum sizes of complete ( 4)-arcs in are obtained. The idea that has been used to do this classification is based on using the algorithm introduced in Section 3 in this paper. Also, this paper establishes the connection between the projective geometry in terms of a complete ( , 4)-arc in and the algebraic characteristics of a plane quartic curve over the field represented by the number of its rational points and inflexion points. In addition, some sizes of complete ( 6)-arcs in the projective plane of order thirteen are established, namely for = 53, 54, 55, 56.
Keywords
Complete arc, Group of complete (k, n)-arc, Inequivalent secant distribution, PG(2, 17), PG(2, 13)
Article Type
Article
How to Cite this Article
Hamed, Zainab Shehab
(2023)
"New sizes of complete (k, 4)-arcs in PG(2,17),"
Baghdad Science Journal: Vol. 20:
Iss.
2, Article 10.
DOI: https://doi.org/10.21123/bsj.2022.6820
