New sizes of complete (k, 4)-arcs in PG(2,17)
Keywords:Complete arc, Group of complete (k,n)-arc, Inequivalent secant distribution, PG(2,17), PG(2,13)
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.
Published Online First 20/9/2022
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