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Year 2012, Volume: 2 Issue: 1, 21 - 27, 21.05.2012

Ziya Akça , İbrahim Günaltılı

Abstract

References

  • Akça, Z. (1991). The construction of the cartesian group plane of order 25, M. Sc thesis, Eskişehir, Turkey: University of Anadolu.
  • Akça, Z. and Kaya, R. (1997). On the subplane of the cartesian group plane of order 25: Proceedings of the X. National Mathematics Conference, Abant Izzet Baysal University, Bolu (Turkey), 1-7.
  • Akça, Z. (2011). A Numerical Computation of (k,3)-arcs in the Left Semifield Plane of order 9, International Electronic Journal of Geometry 4(2), 13-20.
  • Ball, S. (1996). Multiple blocking sets and arcs in finite planes, Journal of London Mathematical Society 54, 581-593.
  • Ball, S. (2005). Hirschfeld J. W. P, Bounds on -arcs and their application to linear codes, Finite Fields and Their Applications 11, 326-336.
  • Coolsaet, K. and Sticker, H. (2010). The complete k-arcs of PG(2,27) and PG(2,29), Journal of Combinatorial Desings 111-130.
  • Daskalov, R.N. and Contreras, M.E.J. (2004). New (k;r)-arcs in the projective plane of order thirteen, Journal of Geometry 80, 10-22.
  • Hirschfeld, J.W.P. (1998). Projective Geometries over Finite Fields, second edition, Oxford University Press. Oxford.
  • Hirschfeld, J.W.P. and Storme, L. (2000). The packing problem in statistics, coding theory and finite projective spaces: update 2001, in: Finite Geometries, Proceedings of the Fourth Isle of Thorns Conference A. Blokhuis, J.W.P. Hirschfeld, D. Jungnickel and J.A. Thas, Eds., Developments in Mathematics, Kluwer Academic Publishers, Boston 201-246.
  • Marcugini, S., Milani, A. and Pambianco, F. (2003). Minimal complete arcs in PG(2,q), q≤29, Journal of combinatorial Mathematics an Combinatorial Computing 47, 19-29.
  • Odabas, A. (2009). Crossed Modules of Algebras with GAP, PhD. thesis, Eskişehir, Turkey: University of Osmangazi.
  • Panella, G. (1965). Una Classe Di Sistemi Cartesiani, Atti Della Accademia Nazionale Lincei Rendiconti 38, 480-485.
  • Thas, J.A. (1975). Some results concerning ((q+1)(n-1),n)-arcs, Journal of Combinatorial Theory Series A 19, 228-232.

CPG(2,25,5) NIN (k,3)-YAYLARI ÜZERİNE

Year 2012, Volume: 2 Issue: 1, 21 - 27, 21.05.2012

Ziya Akça , İbrahim Günaltılı

Abstract

Bu çalışmada, en küçük Kartezyen grup üzerine kurulan 25. mertebeden projektif düzlemdeki ( , 3) k -yayların sınıflaması için bir algoritma ve bazı ( , 3) k -yayların örnekleri verilmektedir.  

Keywords

( 3)-yaylar Projektif düzlem Baer altdüzlemi Kartezyen grup Bilgisayar k

References

  • Akça, Z. (1991). The construction of the cartesian group plane of order 25, M. Sc thesis, Eskişehir, Turkey: University of Anadolu.
  • Akça, Z. and Kaya, R. (1997). On the subplane of the cartesian group plane of order 25: Proceedings of the X. National Mathematics Conference, Abant Izzet Baysal University, Bolu (Turkey), 1-7.
  • Akça, Z. (2011). A Numerical Computation of (k,3)-arcs in the Left Semifield Plane of order 9, International Electronic Journal of Geometry 4(2), 13-20.
  • Ball, S. (1996). Multiple blocking sets and arcs in finite planes, Journal of London Mathematical Society 54, 581-593.
  • Ball, S. (2005). Hirschfeld J. W. P, Bounds on -arcs and their application to linear codes, Finite Fields and Their Applications 11, 326-336.
  • Coolsaet, K. and Sticker, H. (2010). The complete k-arcs of PG(2,27) and PG(2,29), Journal of Combinatorial Desings 111-130.
  • Daskalov, R.N. and Contreras, M.E.J. (2004). New (k;r)-arcs in the projective plane of order thirteen, Journal of Geometry 80, 10-22.
  • Hirschfeld, J.W.P. (1998). Projective Geometries over Finite Fields, second edition, Oxford University Press. Oxford.
  • Hirschfeld, J.W.P. and Storme, L. (2000). The packing problem in statistics, coding theory and finite projective spaces: update 2001, in: Finite Geometries, Proceedings of the Fourth Isle of Thorns Conference A. Blokhuis, J.W.P. Hirschfeld, D. Jungnickel and J.A. Thas, Eds., Developments in Mathematics, Kluwer Academic Publishers, Boston 201-246.
  • Marcugini, S., Milani, A. and Pambianco, F. (2003). Minimal complete arcs in PG(2,q), q≤29, Journal of combinatorial Mathematics an Combinatorial Computing 47, 19-29.
  • Odabas, A. (2009). Crossed Modules of Algebras with GAP, PhD. thesis, Eskişehir, Turkey: University of Osmangazi.
  • Panella, G. (1965). Una Classe Di Sistemi Cartesiani, Atti Della Accademia Nazionale Lincei Rendiconti 38, 480-485.
  • Thas, J.A. (1975). Some results concerning ((q+1)(n-1),n)-arcs, Journal of Combinatorial Theory Series A 19, 228-232.

ON THE (k,3)-ARCS OF CPG(2,25,5)

Year 2012, Volume: 2 Issue: 1, 21 - 27, 21.05.2012

Ziya Akça , İbrahim Günaltılı

Abstract

In the present paper, the algorithm for the classification of the (k,3)- arcs and some examples of the (k,3)-arcs in the projective plane of order 25 over the smallest Cartesian Group are given.

Keywords

(k 3)-arcs Projective plane Baer subplane Cartesian Group Computer search.

References

  • Akça, Z. (1991). The construction of the cartesian group plane of order 25, M. Sc thesis, Eskişehir, Turkey: University of Anadolu.
  • Akça, Z. and Kaya, R. (1997). On the subplane of the cartesian group plane of order 25: Proceedings of the X. National Mathematics Conference, Abant Izzet Baysal University, Bolu (Turkey), 1-7.
  • Akça, Z. (2011). A Numerical Computation of (k,3)-arcs in the Left Semifield Plane of order 9, International Electronic Journal of Geometry 4(2), 13-20.
  • Ball, S. (1996). Multiple blocking sets and arcs in finite planes, Journal of London Mathematical Society 54, 581-593.
  • Ball, S. (2005). Hirschfeld J. W. P, Bounds on -arcs and their application to linear codes, Finite Fields and Their Applications 11, 326-336.
  • Coolsaet, K. and Sticker, H. (2010). The complete k-arcs of PG(2,27) and PG(2,29), Journal of Combinatorial Desings 111-130.
  • Daskalov, R.N. and Contreras, M.E.J. (2004). New (k;r)-arcs in the projective plane of order thirteen, Journal of Geometry 80, 10-22.
  • Hirschfeld, J.W.P. (1998). Projective Geometries over Finite Fields, second edition, Oxford University Press. Oxford.
  • Hirschfeld, J.W.P. and Storme, L. (2000). The packing problem in statistics, coding theory and finite projective spaces: update 2001, in: Finite Geometries, Proceedings of the Fourth Isle of Thorns Conference A. Blokhuis, J.W.P. Hirschfeld, D. Jungnickel and J.A. Thas, Eds., Developments in Mathematics, Kluwer Academic Publishers, Boston 201-246.
  • Marcugini, S., Milani, A. and Pambianco, F. (2003). Minimal complete arcs in PG(2,q), q≤29, Journal of combinatorial Mathematics an Combinatorial Computing 47, 19-29.
  • Odabas, A. (2009). Crossed Modules of Algebras with GAP, PhD. thesis, Eskişehir, Turkey: University of Osmangazi.
  • Panella, G. (1965). Una Classe Di Sistemi Cartesiani, Atti Della Accademia Nazionale Lincei Rendiconti 38, 480-485.
  • Thas, J.A. (1975). Some results concerning ((q+1)(n-1),n)-arcs, Journal of Combinatorial Theory Series A 19, 228-232.
There are 13 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Ziya Akça

İbrahim Günaltılı

Publication Date May 21, 2012
Published in Issue Year 2012 Volume: 2 Issue: 1

Cite

APA Akça, Z., & Günaltılı, İ. (2012). ON THE (k,3)-ARCS OF CPG(2,25,5). Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi - B Teorik Bilimler, 2(1), 21-27.
AMA Akça Z, Günaltılı İ. ON THE (k,3)-ARCS OF CPG(2,25,5). AUBTD-B. May 2012;2(1):21-27.
Chicago Akça, Ziya, and İbrahim Günaltılı. “ON THE (k,3)-ARCS OF CPG(2,25,5)”. Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi - B Teorik Bilimler 2, no. 1 (May 2012): 21-27.
EndNote Akça Z, Günaltılı İ (May 1, 2012) ON THE (k,3)-ARCS OF CPG(2,25,5). Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi - B Teorik Bilimler 2 1 21–27.
IEEE Z. Akça and İ. Günaltılı, “ON THE (k,3)-ARCS OF CPG(2,25,5)”, AUBTD-B, vol. 2, no. 1, pp. 21–27, 2012.
ISNAD Akça, Ziya - Günaltılı, İbrahim. “ON THE (k,3)-ARCS OF CPG(2,25,5)”. Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi - B Teorik Bilimler 2/1 (May 2012), 21-27.
JAMA Akça Z, Günaltılı İ. ON THE (k,3)-ARCS OF CPG(2,25,5). AUBTD-B. 2012;2:21–27.
MLA Akça, Ziya and İbrahim Günaltılı. “ON THE (k,3)-ARCS OF CPG(2,25,5)”. Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi - B Teorik Bilimler, vol. 2, no. 1, 2012, pp. 21-27.
Vancouver Akça Z, Günaltılı İ. ON THE (k,3)-ARCS OF CPG(2,25,5). AUBTD-B. 2012;2(1):21-7.
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