The group action on the finite projective planes of orders 53, 61, 64. (16th November 2020)

• Record Type: Journal Article
• Authors: Makhrib Al-Seraji, Najm Abdulzahra; Alnussairy, Esam A.; Jafar, Zainab Sadiq
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 23:Number 8(2020)
• Page Start: 1573
• Page End: 1582
• Publication Date: 2020-11-16
• Subjects: 11T71; Arcs -- Planes -- Completeness -- Linear Code; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2020.1773020
• Languages: English
• ISSNs: 0972-0529

Abstract

Abstract: The goal of this research is to partition the projective plane PG(2, q ) over Galois Field of order q where q = 53, 61, 64. Classify the group action cyclic groups on PG(2, q ), when the number of points and lines is equal to q 2 + q + 1 which is not a prime have been described. Study the properties of the subsets (orbits, points, lines, planes, triangles) geometrically and algebraically. Also establish the projective codes and arcs with different sizes and degrees by using the program of GAP.