\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

The minimum order of complete caps in $PG(4,4)$

Abstract / Introduction Related Papers Cited by
  • It has been verified that in $PG(4,4)$ the smallest size of complete caps is 20 and that the values from 20 to 41 form the spectrum of possible sizes of complete caps. This result has been obtained by a computer-based proof helped by the non existence of some codes.
    Mathematics Subject Classification: Primary: 51E21, 51E22; Secondary: 94B05.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    D. Bartoli, "Quantum Codes and Related Geometric Properties,'' Ph.D thesis, Università degli Studi di Perugia, Perugia, Italy, 2008.

    [2]

    D. Bartoli, J. Bierbrauer, S. Marcugini and F. Pambianco, Geometric constructions of quantum codes, in "Error-Correcting Codes, Finite Geometries and Cryptography'' (eds. A.A. Bruen and D.L. Wehlau), AMS, (2010), 149-154.

    [3]

    D. Bartoli, S. Marcugini and F. Pambianco, A computer based classification of caps in $PG(3,4)$, in "Rapporto Tecnico - 8/2009,'' Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy, (2009).

    [4]

    D. Bartoli, S. Marcugini and F. PambiancoNew quantum caps in $PG(4,4)$, submitted.

    [5]

    J. Bierbrauer, "Introduction to Coding Theory,'' Chapman and Hall/CRC, Boca Raton, 2005.

    [6]

    J. Bierbrauer, G. Faina, M. Giulietti, S. Marcugini and F. Pambianco, The geometry of quantum codes, Innov. Incidence Geom., 6 (2009), 53-71.

    [7]

    J. Bierbrauer, S. Marcugini and F. Pambianco, The smallest size of a complete cap in $PG(3,7)$, Discrete Math., 306 (2006), 1257-1263.doi: 10.1016/j.disc.2005.06.039.

    [8]

    A. Davydov, G. Faina, S. Marcugini and F. Pambianco, On size of complete caps in projective spaces $PG(n,q)$ and arcs in planes $PG(2,q)$, J. Geom., 94 (2009), 31-58.doi: 10.1007/s00022-009-0009-3.

    [9]

    A. A. Davydov, S. Marcugini and F. Pambianco, Complete caps in projective spaces $PG(n,q)$, J. Geom., 80 (2004), 23-30.doi: 10.1007/s00022-004-1778-3.

    [10]

    G. Faina and F. Pambianco, On the spectrum of the values $k$ for which a complete $k$-cap in $PG(n,q)$ exists, J. Geom., 62 (1998), 84-98.doi: 10.1007/BF01237602.

    [11]

    M. GrasslBounds on the minimum distance of linear codes, available online at http://www.codetables.de

    [12]

    R. Hill, Caps and codes, Discrete Math., 22 (1978), 111-137.doi: 10.1016/0012-365X(78)90120-6.

    [13]

    S. Marcugini, A. Milani and F. Pambianco, Complete arcs in $PG(2,25)$: the spectrum of the sizes and the classification of the smallest complete arcs, Discrete Math., 307 (2007), 739-747.doi: 10.1016/j.disc.2005.11.094.

    [14]

    F. Pambianco and L. Storme, Small complete caps in spaces of even characteristic, J. Combin. Theory Ser. A, 75 (1996), 70-84.doi: 10.1006/jcta.1996.0064.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(129) Cited by(0)

Access History

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return