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Computer search for small complete caps

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Abstract

A computer search method for finding small complete caps inPG(d,q) is considered. The problem is formulated as a combinatorial optimization problem to which record-to-record travel, a stochastic local search method, is applied. Several new complete caps are found and upper bounds on the number of points in the smallest complete caps inPG(d,q) are tabulated for small parameters.

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References

  1. E. Aarts andJ. K. Lenstra (Eds.), “Local Search in Combinatorial Optimization,” Wiley, New York, 1997.

    Google Scholar 

  2. A. A.Davydov and P. R. J.Österg»rd, Recursive constructions of complete caps, submitted for publication.

  3. G. Dueck, New optimization heuristics: The great deluge algorithm and record-to-record travel,J. Comput. Phys. 104 (1993), 86–92.

    Google Scholar 

  4. G. Faina andF. Pambianco, On the spectrum of the valuesk for which a completek-cap in PG(n, q) exists,J. Geom. 62 (1998), 84–98.

    Google Scholar 

  5. J. W. P. Hirschfeld, “Finite Projective Spaces of Three Dimensions,” Oxford University Press, Oxford, 1985.

    Google Scholar 

  6. J. W. P. Hirschfeld, “Projective Geometries over Finite Fields,” 2nd ed., Clarendon, Oxford, 1998.

    Google Scholar 

  7. J. W. P.Hirschfeld and L.Storme, The packing problem in statistics, coding theory, and finite projective spaces,J. Statist. Plann. Inference, to appear.

  8. S. Marcugini, A. Milani, andF. Pambianco, “A Computer Search for Complete Arcs in PG(2,q),q<- 128,” Technical Report 18/95, Università degli Studi di Perugia, Italy, 1995.

    Google Scholar 

  9. F. Pambianco andL. Storme, Small complete caps in spaces of even characteristic,J. Combin. Theory. Ser. A 75 (1996), 70–84.

    Google Scholar 

  10. G. F. Royle, An orderly algorithm and some applications in finite geometry,Discrete Math. 185 (1998), 105–115.

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Computer Science and Engineering, Helsinki University of Technology, P.O. Box 5400, 02015, HUT, Finland

    Patric R. J. Österg»rd

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  1. Patric R. J. Österg»rd
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Additional information

This research was supported by the Academy of Finland.

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Österg»rd, P.R.J. Computer search for small complete caps. J Geom 69, 172–179 (2000). https://doi.org/10.1007/BF01237484

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  • DOI: https://doi.org/10.1007/BF01237484

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