In this work, we construct projectively distinct (k,3)-arcs in the projective plane PG(2,9) by applying a geometrical method. The cubic curves have been been constructed by using the general equation of the cubic.         We found that there are complete (13,3)-arcs, complete (15,3)-arcs and we found that the only (16,3)-arcs lead to maximum completeness

A (k,n)-arc is a set of k points of PG(2,q) for some n, but not n + 1 of them, are collinear. A (k,n)-arc is complete if it is not contained in a (k + 1,n)-arc. In this paper we construct complete (kn,n)-arcs in PG(2,5), n = 2,3,4,5, by geometric method, with the related blocking sets and projective codes.

   In this paper,we construct complete (kn,n)-arcs in the projective plane PG(2,11),  n = 2,3,…,10,11  by geometric method, with the related blocking sets and projective codes.
 

            The article describes a certain computation method of -arcs to construct the number of distinct -arcs in  for . In this method, a new approach employed to compute the number of -arcs and the number of distinct arcs respectively. This approach is based on choosing the number of inequivalent classes } of -secant distributions that is the number of 4-secant, 3-secant, 2-secant, 1-secant and 0-secant in each process. The maximum size of -arc that has been constructed by this method is . The new method is a new tool to deal with the programming difficulties that sometimes may lead to programming problems represented by the increasing number of arcs. It is essential to reduce the established number of -arcs in each cons

  The purpose of this paper is  to find an arc of degree five in 31 ,29),(2, =qqPG , with stabilizer group of type dihedral group of degree five 5 D and arcs of degree six and ten with stabilizer groups of type alternating group of degree five 5 A ,  then study the effect of  5 D and 5A on the points of projective plane. Also, find a pentastigm which has collinear diagonal points.

A (b,t)-blocking set B in PG(2,q) is set of b points such that every line of PG(2,q) intersects B in at least t points and there is a line intersecting B in exactly t points. In this paper we construct a minimal (b,t)-blocking sets, t = 1,2,3,4,5 in PG(2,5) by using conics to obtain complete arcs and projective codes related with them.

This paper presents a point multiplication processor over the binary field GF (2²³³) with internal registers integrated within the point-addition architecture to enhance the Performance Index (PI) of scalar multiplication. The proposed design uses one of two types of finite field multipliers, either the Montgomery multiplier or the interleaved multiplier supported by the additional layer of internal registers. Lopez Dahab coordinates are used for the computation of point multiplication on Koblitz Curve (K-233bit). In contrast, the metric used for comparison of the implementations of the design on different types of FPGA platforms is the Performance Index.

The first approach attains a performance index

Plane cubics curves may be classified up to isomorphism or projective equivalence. In this paper, the inequivalent elliptic cubic curves which are non-singular plane cubic curves have been classified projectively over the finite field of order nineteen, and determined if they are complete or incomplete as arcs of degree three. Also, the maximum size of a complete elliptic curve that can be constructed from each incomplete elliptic curve are given.

In this work, new kinds of blocking sets in a projective plane over Galois field PG(2,q) can be obtained. These kinds are called the complete blocking set and maximum blocking set. Some results can be obtained about them.

              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.