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:

sbReference
(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 + 9b = 2r[2]
3b2 + 4b = 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).” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_CCapsM5.html

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