This research is concerned with the study of the projective plane over a finite field . The main purpose is finding partitions of the projective line PG( ) and the projective plane PG( ) , in addition to embedding PG(1, ) into PG( ) and PG( ) into PG( ). Clearly, the orbits of PG( ) are found, along with the cross-ratio for each orbit. As for PG( ), 13 partitions were found on PG( ) each partition being classified in terms of the degree of its arc, length, its own code, as well as its error correcting. The last main aim is to classify the group actions on PG( ).
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
... Show MoreThe aim of this paper is to introduce the definition of projective 3-space over Galois field GF(q), q = pm, for some prime number p and some integer m.
Also the definitions of (k,n)-arcs, complete arcs, n-secants, the index of the point and the projectively equivalent arcs are given.
Moreover some theorems about these notations are proved.
In this paper we study the concepts of δ-small M-projective module and δ-small M-pseudo projective Modules as a generalization of M-projective module and M-Pseudo Projective respectively and give some results.
In this paper we study the concepts of δ-small M-projective module and δ-small M-pseudo projective Modules as a generalization of M-projective module and M-Pseudo Projective respectively and give some results.
Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
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In this paper, we introduce the concept of e-small M-Projective modules as a generalization of M-Projective modules.
The aim of this paper is to construct the (k,r)-caps in the projective 3-space PG(3,p) over Galois field GF(4). We found that the maximum complete (k,2)-cap which is called an ovaloid , exists in PG(3,4) when k = 13. Moreover the maximum (k,3)-caps, (k,4)-caps and (k,5)-caps.
The main aim of this paper is to introduce the relationship between the topic of coding theory and the projective plane of order three. The maximum value of size of code over finite field of order three and an incidence matrix with the parameters, (length of code), (minimum distance of code) and (error-correcting of code ) have been constructed. Some examples and theorems have been given.
The main aims of this research is to find the stabilizer groups of a cubic curves over a finite field of order , studying the properties of their groups and then constructing the arcs of degree which are embedding in a cubic curves of even size which are considering as the arcs of degree . Also drawing all these arcs.
In this paper the queuing system (M/Er/1/N) has been considered in equilibrium. The method of stages introduced by Erlang has been used. The system of equations which governs the equilibrium probabilities of various stages has been given. For general N the probability of j stages of service are left in the system, has been introduced. And the probability for the empty system has been calculated in the explicit form.