Classification of Arcs in Finite Projective Plane of Order Sixteen

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


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.


words: projective plane, arcs, code

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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)



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