Large Caps in PG(4, b)
In [1], [2], and[3], Bierbrauer and Edel construct large caps in the projective space PG(4, b), and therefore [s, s−5, 4]-codes over Fb. The following values of s can be achieved for b ≥ 5:
| s | b | Reference |
| (5b2 − 2b−7)/2 | b≡1 mod 8 | [1] |
| (5b2 − 8b−13)/2 | b≡3 mod 8 | [1] |
| (5b2 − 6b−11)/2 | b≡5 mod 8 | [1] |
| (5b2 − 4b−9)/2 | b≡7 mod 8 | [1] |
| 2b2 + b + 9 | b = 2r | [2] |
| 3b2 + 4 | b = 2r with r odd | [3] |
See also
References
| [1] | Jürgen Bierbrauer and Yves Edel. A family of caps in projective 4-space in odd characteristic. Finite Fields and Their Applications, 6(4):283–293, October 2000. doi:10.1006/ffta.2000.0290 |
| [2] | Jürgen Bierbrauer and Yves Edel. A family of caps in projective 4-space in characteristic 2. In Proceedings of the Southeastern Conference, volume 141 of Congressus Numerantium, pages 199–201, 1999. |
| [3] | Yves Edel and Jürgen Bierbrauer. Caps of order 3q2 in affine 4-space in characteristic 2. Finite Fields and Their Applications, 10(2):168–182, April 2004. doi:10.1016/S1071-5797(03)00050-9 |
| [4] | James W. P. Hirschfeld and Leo Storme. The packing problem in statistics, coding theory and finite projective spaces: Update 2001. In Finite Geometries, volume 3 of Developments in Mathematics, pages 201–246. Kluwer Academic Publishers, 2001. |
| [5] | 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. “Large Caps in PG(4, b).”
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Version: 2024-09-05.
http://mint.sbg.ac.at/desc_CCapsM5.html