Classification of Arcs in Finite Projective Plane of Order Sixteen

Najm A. Al-Seraji; Riyam A. Al-Ogali

doi:10.23851/mjs.v29i1.184

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

Bose R.C, 1947," Mathematical theory of the symmetrical factorial design" Sankhya, 8:107-166.

Segre B ,1954, "Sulle ovali nei piani lineari finiti." Atti Accad. Naz. Lincei Rend., 17:1-2.

Goppa V. D, 1981, "Codes on algebraic curves" Soviet Math. Dokl., 24:170-172.

Hirschfeld J. W. P., (1998), Projective geometries over finite fields, 2nd Edition, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York.

Thomas A. D. and Wood G. V., (1980), Group tables, Shiva Mathematics Series, Series 2., Devon Print Group, Exeter, Devon, UK.

Al-Zangana E. M., (2011), The geometry of the plane of order nineteen and its application to error-correcting codes, Ph.D. thesis, University of Sussex, United Kingdom.

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).

N.A.M. Al-Seraji, Classification of the Projective line over Galois Field of order sixteen, Al-Mustansiriyah journal of Science, Vol. 24, No.6 ,(2014)

Downloads

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”, Al-Mustansiriyah Journal of Science, vol. 29, no. 1, pp. 138–149, Oct. 2018.

Issue

Vol. 29 No. 1 (2018)

Section

Mathematics

License

Articles accepted for publication in Al-Mustansiriyah Journal of Science (MJS) are protected under the Creative Commons Attribution 4.0 International License (CC-BY-NC). Authors of accepted articles are requested to sign a copyright release form prior to their article being published. All authors must agree to the submission, sign copyright release forms, and agree to be included in any correspondence between MJS and the authors before submitting a work to MJS. For personal or educational use, permission is given without charge to print or create digital copies of all or portions of a MJS article. However, copies must not be produced or distributed for monetary gain. It is necessary to respect the copyright of any parts of this work that are not owned by MJS.