Classification of Arcs in Finite Projective Plane of Order Sixteen

Authors

  • Najm A. Al-Seraji Department of Mathematics, College of Science, Mustansiriyah University
  • Riyam A. Al-Ogali Department of Mathematics, College of Science, Mustansiriyah University

DOI:

https://doi.org/10.23851/mjs.v29i1.184

Keywords:

words, projective plane, arcs, code

Abstract

The aim of the paper is to classify certain geometric structures, called arcs. The main computing tool is the mathematical programming language GAP. In the plane PG(2,16),the important arcs are called complete and are those that cannot be increased to a larger arc. So far, all arcs up to size eighteen have been classified. Each of these arcs gives rise to an error-correcting code that corrects the maximum possible number of errors for its length.

References

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N.A.M. Al-Seraji, The Geometry of The Plane of order Seventeen and its Application to Error-correcting Codes , Ph.D. Thesis, University of Sussex, UK., (2010) .

N.A.M. Al-Seraji, Partitions by Subgeometries of Projective Plane Over Finite Field of Order Sixteen, AL-Mustansiriyah Journal of Science, Vol. 22, No.4,(2011).

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Published

2018-10-31

How to Cite

[1]
N. A. Al-Seraji and R. A. Al-Ogali, “Classification of Arcs in Finite Projective Plane of Order Sixteen”, MJS, vol. 29, no. 1, pp. 138–149, Oct. 2018.

Issue

Section

Mathematics