Hill Cap

With a size of 56 the Hill-cap [1] is the largest possible cap in the projective space PG(5, 3). It has an affine sub-cap of size 45, which is the largest possible cap in the affine space AG(5, 3) [2].

The projective cap corresponds directly to a linear [56, 50, 4]-code over F3.

See Also

References

[1]Raymond Hill.
On the largest size of cap in S5,3.
Rendiconti della Accademia Nazionale dei Lincei, 54:378–384, 1973.
[2]Yves Edel, S. Ferret, Ivan N. Landgev, and Leo Storme.
The classification of the largest caps in AG(5, 3).
Journal of Combinatorial Theory, Series A, 99(1):95–110, July 2002.
doi:10.1006/jcta.2002.3261
[3]Jürgen Bierbrauer.
Introduction to Coding Theory.
Discrete Mathematics and its Applications. Chapman & Hall/CRC, Boca Raton, London, New York, Washington D.C., 2004.
MR2079734 (2005f:94001)

Copyright

Copyright © 2004, 2005, 2006, 2007, 2008, 2009, 2010 by Rudolf Schürer and Wolfgang Ch. Schmid.
Cite this as: Rudolf Schürer and Wolfgang Ch. Schmid. “Hill Cap.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_CHillCap.html

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