Journal of Discrete Mathematics

Volume 2013, Article ID 628952, 7 pages

http://dx.doi.org/10.1155/2013/628952

Research Article

## Improved Bounds on

Department of Mathematics, Technical University of Gabrovo, 5300 Gabrovo, Bulgaria

Received 8 November 2012; Accepted 3 February 2013

Academic Editor: Aziz Moukrim

Copyright © 2013 Rumen Daskalov and Elena Metodieva. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Linked References

- R. C. Bose, “Mathematical theory of the symmetrical factorial design,”
*Sankhyā*, vol. 8, pp. 107–166, 1947. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - A. Barlotti,
*Some Topics in Finite Geometrical Structures*, Institute of Statistics Mimeo Series no. 439, University of Carollina, 1965. - J. W. P. Hirschfeld,
*Projective Geometries over Finite Fields*, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, NY, USA, 2nd edition, 1998. View at MathSciNet - J. W. P. Hirschfeld and L. Storme, “The packing problem in statistics, coding theory and finite projective spaces: update 2001,” in
*Finite Geometries*, vol. 3 of*Developments in Mathematics*, pp. 201–246, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - R. Daskalov, “On the existence and the nonexistence of some (
*k, r*)-arcs in $PG$(2, 17),” in*Proceedings of the 9th International Workshop on Algebraic and Combinatorial Coding Theory*, pp. 95–100, Kranevo, Bulgaria, June 2004. - R. Daskalov and E. Metodieva, “New $(k,r)$-arcs in $\mathrm{PG}(2,17)$ and the related optimal linear codes,”
*Mathematica Balkanica. New Series*, vol. 18, no. 1-2, pp. 121–127, 2004. View at Google Scholar · View at MathSciNet - M. Braun, A. Kohnert, and A. Wassermann, “Construction of $(n,r)$-arcs in $\mathrm{PG}(2,q)$,”
*Innovations in Incidence Geometry*, vol. 1, pp. 133–141, 2005. View at Google Scholar · View at MathSciNet - S. Ball and J. W. P. Hirschfeld, “Bounds on $(n,r)$-arcs and their application to linear codes,”
*Finite Fields and Their Applications*, vol. 11, no. 3, pp. 326–336, 2005. View at Publisher · View at Google Scholar · View at MathSciNet - A. Kohnert, “Arcs in the projective planes,” Online tables, http://www.algorithm.uni-bayreuth.de/en/research/Coding_Theory/PG_arc_table/index.html.
- R. Daskalov and E. Metodieva, “New $(n,r)$-arcs in $\mathrm{PG}(2,17)$, $\mathrm{PG}(2,19)$ and $\mathrm{PG}(2,23)$,”
*Problemy Peredachi Informatsii*, vol. 47, no. 3, pp. 3–9, 2011, English translation:*Problems of Information Transmission*, vol. 47, no. 3, pp. 217–223, 2011. View at Google Scholar · View at MathSciNet - S. Ball, “Three-dimensional linear codes,” Online table, http://www-ma4.upc.edu/~simeon/.
- H. A. Barker, “Sum and product tables for Galois fields,”
*International Journal of Mathematical Education in Science and Technology*, vol. 17, no. 4, pp. 473–485, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - R. Daskalov and E. Metodieva, “New large arcs in PG(2,25) and PG(2,27),” in
*Proceedings of the 13th International Workshop on Algebraic and Combinatorial Coding Theory*, pp. 130–135, Pomorie, Bulgaria, June 2012. - R. Hill, “Optimal linear codes,” in
*Cryptography and Coding, II (Cirencester, 1989)*, vol. 33, pp. 75–104, Oxford University Press, New York, NY, USA, 1992. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - S. Ball, “Multiple blocking sets and arcs in finite planes,”
*Journal of the London Mathematical Society*, vol. 54, no. 3, pp. 581–593, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - R. Daskalov, “On the maximum size of some $(k,r)$-arcs in $\mathrm{PG}(2,q)$,”
*Discrete Mathematics*, vol. 308, no. 4, pp. 565–570, 2008. View at Publisher · View at Google Scholar · View at MathSciNet - J. R. M. Mason, “On the maximum sizes of certain ($k,n$)-arcs in finite projective geometries,”
*Mathematical Proceedings of the Cambridge Philosophical Society*, vol. 91, no. 2, pp. 153–169, 1982. View at Publisher · View at Google Scholar · View at MathSciNet - A. Barlotti, “Sui $\{k;\hspace{0.17em}n\}$-archi di un piano lineare finito,”
*Bollettino della Unione Matematica Italiana*, vol. 11, pp. 553–556, 1956. View at Google Scholar · View at MathSciNet - S. Ball, “On nuclei and blocking sets in Desarguesian spaces,”
*Journal of Combinatorial Theory. Series A*, vol. 85, no. 2, pp. 232–236, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet