The Possibility of Applying Rumen Research at the Projective Plane PG (2,17)

Shaymaa Haleem Ibrahim,Nada Yassen Kasm

doi:10.5539/mas.v13n8p150

Abstract

One of the main objectives of this research is to use a new theoretical method to find arcs and Blocking sets. This method includes the deletion of a set of points from some lines under certain conditions explained in a paragraph 2.In this paper we were able to improve the minimum constraint of the (256,16) &ndash; arc in the projection plane PG(2,17).Thus , we obtained a new {50,2}-blocking set for size Less than 3q , and according to the theorem (1.3.1),we obtained the linear 257,3,24117&nbsp;&nbsp;&nbsp; code, theorem( 2.1.1 ) giving some examples on arcs of the Galois field GF(q);q=17.&quot;

Highlights

Numerous studies in algebraic geometry have been found in various sources, including obtaining the optimal size of the projection plane by intersecting the tangent in PG(2,q)(Yahya &Salim, 2019,pp.312-333), the applications of algebraic geometry, the coding methods, and obtaining the optimal codes( Kasm,& Hamad,2019,pp.130-139) (Nilsson, Johansson, & Wagner, 2019, pp. 238-258)
Definition(1.2.3):Let M be a set of points in any plane An i-secant is a line meeting M in exactly I points .Define ti as the number of i-secants to a set M. ( Hirschfeld,1979) ." Theorem(1.2.4): Let B be a double blocking set in the projection plane PG (2, q):
2) Improvement of linear codes in the projection plane PG (2,17) Theorem (2.1.1) improvement Linear code [256,3,240]17 to [257,3,240]17

Summary

Introduce the Problem

Numerous studies in algebraic geometry have been found in various sources, including obtaining the optimal size of the projection plane by intersecting the tangent in PG(2,q)(Yahya &Salim , 2019,pp.312-333), the applications of algebraic geometry, the coding methods, and obtaining the optimal codes( Kasm,& Hamad,2019,pp.130-139) (Nilsson, Johansson, & Wagner, 2019, pp. 238-258). Numerous studies in algebraic geometry have been found in various sources, including obtaining the optimal size of the projection plane by intersecting the tangent in PG(2,q)(Yahya &Salim , 2019,pp.312-333), the applications of algebraic geometry, the coding methods, and obtaining the optimal codes( Kasm,& Hamad,2019,pp.130-139) Let GF(q) denote the Galois field of q elements and V (3, q) be the vector space of row vectors of length three with entries in GF(q). Let PG(2, q) be the corresponding projective plane( Hirschfeld,1979) ."

Explore Importance of the Problem

Describe Relevant Scholarship

Geometric Builiding Approach

Conclusion