Preferred Language
Articles
/
jih-825
Some Results on The Complete Arcs in Three Dimensional Projective Space Over Galois Field
...Show More Authors

        The 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.

 

View Publication Preview PDF
Quick Preview PDF
Publication Date
Thu Apr 27 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Complete Arcs in Projective Plane PG (2,11) Over Galois field
...Show More Authors

    In this work, we construct complete (K, n)-arcs in the projective plane over Galois field GF (11), where 12 2 ≤ ≤ n  ,by using geometrical method (using the union of some maximum(k,2)- Arcs , we found (12,2)-arc, (19,3)-arc , (29,4)-arc, (38,5)-arc , (47,6)-arc, (58,7)-arc, (68,6)-arc, (81,9)-arc, (96,10)-arc, (109,11)-arc, (133,12)-arc, all of them are complete arc in PG(2, 11) over GF(11).  

View Publication Preview PDF
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)
...Show More Authors

  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

View Publication Preview PDF
Publication Date
Thu May 11 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
On Projective 3-Space Over Galois Field
...Show More Authors

        The purpose of this paper is to give the definition of projective 3-space PG(3,q) over Galois field GF(q), q = pm for some prime number p and some integer m.

        Also, the definition of the plane in PG(3,q) is given and state the principle of duality.

        Moreover some theorems in PG(3,q) are proved.

View Publication Preview PDF
Publication Date
Sun Apr 30 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Classification and Construction of (k,3)-Arcs on Projective Plane Over Galois Field GF(7)
...Show More Authors

  The purpose of this work is to study the classification and construction of (k,3)-arcs in the projective plane PG(2,7). We found that there are two (5,3)-arcs, four (6,3)-arcs, six (7,3)arcs, six (8,3)-arcs, seven (9,3)-arcs, six (10,3)-arcs and six (11,3)-arcs.         All of these arcs are incomplete.         The number of distinct (12,3)-arcs are six, two of them are complete.         There are four distinct (13,3)-arcs, two of them are complete and one (14,3)-arc which is incomplete.         There exists one complete (15,3)-arc.
 

View Publication Preview PDF
Publication Date
Sun Apr 30 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Classification and Construction of (k,3)-Arcs on Projective Plane Over Galois Field GF(9)
...Show More Authors

  In this work, we construct and classify the projectively distinct (k,3)-arcs in PG(2,9), where k ≥ 5, and prove that the complete (k,3)-arcs do not exist, where 5 ≤ k ≤ 13. We found that the maximum complete (k,3)-arc in PG(2,q) is the (16,3)-arc and the minimum complete (k,3)-arc in PG(2,q) is the (14,3)-arc. Moreover, we found the complete (k,3)-arcs between them.

View Publication Preview PDF
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
...Show More Authors

        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

View Publication Preview PDF
Publication Date
Mon Aug 01 2022
Journal Name
Baghdad Science Journal
Subgroups and Orbits by Companion Matrix in Three Dimensional Projective Space
...Show More Authors

The aim of this paper is to construct cyclic subgroups of the projective general linear group over  from the companion matrix, and then form caps of various degrees in . Geometric properties of these caps as secant distributions and index distributions are given and determined if they are complete. Also, partitioned of  into disjoint lines is discussed.

View Publication Preview PDF
Scopus (8)
Crossref (4)
Scopus Clarivate Crossref
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)
...Show More Authors

   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. 

View Publication Preview PDF
Publication Date
Wed Dec 01 2021
Journal Name
Baghdad Science Journal
A complete (48, 4)-arc in the Projective Plane Over the Field of Order Seventeen
...Show More Authors

            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 More
View Publication Preview PDF
Scopus (2)
Crossref (1)
Scopus Clarivate Crossref
Publication Date
Wed May 31 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Sets of Subspaces of a Projective Plane PG(2,q) Over Galois Field GF(q)
...Show More Authors

       In this thesis, some sets of subspaces of projective plane PG(2,q) over Galois field GF(q) and the relations between them by some theorems and examples can be shown.
 

View Publication Preview PDF