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- Title
New sizes of complete (k, 4)-arcs in PG(2,17).
- Authors
Hamed, Zainab Shehab
- Abstract
In this paper, the packing problem for complete (𝑘, 4)-arcs in 𝑃𝐺(2, 17) is partially solved. The minimum and the maximum sizes of complete (𝑘, 4)-arcs in 𝑃𝐺(2, 17) 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 (𝑘, 4)-arc 𝐾 in 𝑃𝐺(2, 17) and the algebraic characteristics of a plane quartic curve over the field 𝐹17 represented by the number of its rational points and inflexion points. In addition, some sizes of complete (𝑘, 6)-arcs in the projective plane of order thirteen are established, namely for 𝑘 = 53, 54, 55, 56.
- Subjects
PROJECTIVE geometry; PLANE curves; PROJECTIVE planes; RATIONAL numbers; RATIONAL points (Geometry)
- Publication
Baghdad Science Journal, 2023, Vol 20, Issue 2, p502
- ISSN
2078-8665
- Publication type
Article
- DOI
10.21123/bsj.2022.6820