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
[3, Theorem 16.65]
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: 2024-09-05.
http://mint.sbg.ac.at/desc_CHillCap.html