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ijs-7385
Classification of the Projective Line over Galois Field of Order 31
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Our research is related to the projective line over the finite field, in this paper, the main purpose is to classify the sets of size K on the projective line PG (1,31), where K = 3,…,7 the number of inequivalent K-set with stabilizer group by using the GAP Program is computed.

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Publication Date
Thu May 11 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Construction and Reverse Construction of the Complete Arcs in the Projective 3-Space Over Galois Field GF(2)
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  The main purpose of this work is to find the complete arcs in the projective 3-space over Galois field GF(2), which is denoted by PG(3,2), by two methods and then we compare between the two methods

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Publication Date
Sun Dec 04 2016
Journal Name
Baghdad Science Journal
Classification of Elliptic Cubic Curves Over The Finite Field of Order Nineteen
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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.

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Publication Date
Sun Aug 13 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Construction of Complete (k,n)-arcs in the Projective Plane PG(2,11) Over Galois Field GF(11), 3 ï‚£ n ï‚£ 11
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        The purpose of this work is to construct complete (k,n)-arcs in the projective 2-space PG(2,q) over Galois field GF(11) by adding some points of index zero to complete (k,n–1)arcs 3 ï‚£ n ï‚£ 11.         A (k,n)-arcs is a set of k points no n + 1 of which are collinear.         A (k,n)-arcs is complete if it is not contained in a (k + 1,n)-arc

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Publication Date
Mon Apr 24 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Groups Effect of Types 5 D and 5 Α on The Points of Projective Plane Over 31 ,29,F =qq
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  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.

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Publication Date
Sun May 14 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
A Complete (k,r)-Cap in PG(3,p) Over Galois Field GF(4)
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   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. 

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Publication Date
Tue Nov 30 2021
Journal Name
Iraqi Journal Of Science
Certain Types of Linear Codes over the Finite Field of Order Twenty-Five
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The aim of the paper is to compute projective maximum distance separable codes, -MDS of two and three dimensions with certain lengths and Hamming weight distribution from the arcs in the projective line and plane over the finite field of order twenty-five. Also, the linear codes generated by an incidence matrix of points and lines of  were studied over different finite fields.  

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Publication Date
Sun Jun 20 2021
Journal Name
Baghdad Science Journal
Projective MDS Codes Over GF(27)‎
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MDS code is a linear code that achieves equality in the Singleton bound, and projective MDS (PG-MDS) is MDS code with independents property of any two columns of its generator matrix.   In this paper, elementary methods for modifying a PG-MDS code of dimensions 2, 3, as extending and lengthening, in order to find new incomplete PG-MDS codes have been used over . Also, two complete PG-MDS codes over  of length  and 28 have been found.

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Publication Date
Wed Oct 31 2018
Journal Name
Iraqi Journal Of Science
Some application of coding theory in the projective plane of order three
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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.

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Publication Date
Fri Jan 26 2024
Journal Name
Iraqi Journal Of Science
On the Size of Complete Arcs in Projective Space of Order 17
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The main goal of this paper is to show that a
-arc in
and
is subset of a twisted cubic, that is, a normal rational curve. The maximum size of an arc in a projective space or equivalently the maximum length of a maximum distance separable linear code are classified. It is then shown that this maximum is
for all dimensions up to
.

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Publication Date
Sun Jul 29 2018
Journal Name
Iraqi Journal Of Science
On the Embedding of an Arc Into a Cubic Curves in a Finite Projective Plane of Order Five
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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.

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