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bsj-6820
New sizes of complete (k, 4)-arcs in PG(2,17)
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              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.

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Publication Date
Sun May 28 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Maximum Complete (k,n)-Arcs in the Projective Plane PG(2,4) By Geometric Method
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A (k,n)-arc A in a finite projective plane PG(2,q) over Galois field GF(q), q=pⁿ for same prime number p and some integer n≥2, is a set of k points, no n+1 of which are collinear.  A (k,n)-arc is complete if it is not contained in a(k+1,n)-arc.  In this paper, the maximum complete (k,n)-arcs, n=2,3 in PG(2,4) can be constructed from the equation of the conic.

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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
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
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    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).  

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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
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            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

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Publication Date
Wed Aug 10 2011
Journal Name
Ibn Al- Haitham J. For Pure & Appl. S Ci.
A Complete (k,r)-Cap in PG(3,p) Over Galois Field GF(4)
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The aim of t his p aper is t o const ruct t he (k,r)-caps in t he p rojective 3-sp ace PG(3,p ) over Galois field GF(4). We found t hat t he maximum comp let e (k,2)-cap which is called an ovaloid, exist s in PG(3,4) when k = 13. Moreover t he maximum (k,3)-cap s, (k,4)-cap s and (k,5)-caps.

Publication Date
Tue Jan 01 2013
Journal Name
Journal Of College Of Education
The Construction of Complete (k, n)-arcs in 3-Dimensional Projective Space Over Galois Field GF (4)
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In this work, we construct the projectively distinct (k, n)-arcs in PG (3, 4) over Galois field GF (4), where k 5, and we found that the complete (k, n)-arcs, where 3 n 21, moreover we prove geometrically that the maximum complete (k, n)-arc in PG (3, 4) is (85, 21)-arc. 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)-arcs

Publication Date
Thu Apr 27 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Construction of (k,3)-Arcs in PG(2,9) by Using Geometrical Method
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  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

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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 01 2013
Journal Name
Ibn Al-haitham Journal For Pure And Applied Science
The Construction of (k, 3)-Arcs in PG (2, 9) by Using Geometrical Method
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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

Publication Date
Fri Mar 17 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Construction of Minimal (b,t)-Blocking Sets Containing Conics in PG(2,5) with the Complete Arcs and Projective Codes Related with Them
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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.

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