A complete (48, 4)-arc in the Projective Plane Over the Field of Order Seventeen

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 inequival...

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Autores principales:	zainab Shehab Hamed, J.W. Hirschfeld
Formato:	article
Lenguaje:	AR EN
Publicado:	College of Science for Women, University of Baghdad 2021
Materias:	Projective space, (k; n)-arc, distinct secant distribution, complete arc, and Group Science Q
Acceso en línea:	https://doaj.org/article/555b2bfab3424903a85a87389c9a354d
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spelling	oai:doaj.org-article:555b2bfab3424903a85a87389c9a354d2021-12-04T16:12:52ZA complete (48, 4)-arc in the Projective Plane Over the Field of Order Seventeen10.21123/bsj.2021.18.4.12382078-86652411-7986https://doaj.org/article/555b2bfab3424903a85a87389c9a354d2021-12-01T00:00:00Zhttps://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/5193https://doaj.org/toc/2078-8665https://doaj.org/toc/2411-7986 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 construction especially for large value of and then reduce the running time of the calculation. Therefore, it allows to decrease the memory storage for the calculation processes. This method’s effectiveness evaluation is confirmed by the results of the calculation where a largest size of complete -arc is constructed. This research’s calculation results develop the strategy of the computational approaches to investigate big sizes of arcs in where it put more attention to the study of the number of the inequivalent classes of -secants of -arcs in which is an interesting aspect. Consequently, it can be used to establish a large value of . zainab Shehab HamedJ.W. HirschfeldCollege of Science for Women, University of BaghdadarticleProjective space, (k; n)-arc, distinct secant distribution, complete arc, and GroupScienceQARENBaghdad Science Journal, Vol 18, Iss 4 (2021)
institution	DOAJ
collection	DOAJ
language	AR EN
topic	Projective space, (k; n)-arc, distinct secant distribution, complete arc, and Group Science Q
spellingShingle	Projective space, (k; n)-arc, distinct secant distribution, complete arc, and Group Science Q zainab Shehab Hamed J.W. Hirschfeld A complete (48, 4)-arc in the Projective Plane Over the Field of Order Seventeen
description	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 construction especially for large value of and then reduce the running time of the calculation. Therefore, it allows to decrease the memory storage for the calculation processes. This method’s effectiveness evaluation is confirmed by the results of the calculation where a largest size of complete -arc is constructed. This research’s calculation results develop the strategy of the computational approaches to investigate big sizes of arcs in where it put more attention to the study of the number of the inequivalent classes of -secants of -arcs in which is an interesting aspect. Consequently, it can be used to establish a large value of .
format	article
author	zainab Shehab Hamed J.W. Hirschfeld
author_facet	zainab Shehab Hamed J.W. Hirschfeld
author_sort	zainab Shehab Hamed
title	A complete (48, 4)-arc in the Projective Plane Over the Field of Order Seventeen
title_short	A complete (48, 4)-arc in the Projective Plane Over the Field of Order Seventeen
title_full	A complete (48, 4)-arc in the Projective Plane Over the Field of Order Seventeen
title_fullStr	A complete (48, 4)-arc in the Projective Plane Over the Field of Order Seventeen
title_full_unstemmed	A complete (48, 4)-arc in the Projective Plane Over the Field of Order Seventeen
title_sort	complete (48, 4)-arc in the projective plane over the field of order seventeen
publisher	College of Science for Women, University of Baghdad
publishDate	2021
url	https://doaj.org/article/555b2bfab3424903a85a87389c9a354d
work_keys_str_mv	AT zainabshehabhamed acomplete484arcintheprojectiveplaneoverthefieldoforderseventeen AT jwhirschfeld acomplete484arcintheprojectiveplaneoverthefieldoforderseventeen AT zainabshehabhamed complete484arcintheprojectiveplaneoverthefieldoforderseventeen AT jwhirschfeld complete484arcintheprojectiveplaneoverthefieldoforderseventeen
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A complete (48, 4)-arc in the Projective Plane Over the Field of Order Seventeen

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