Product of Two Projective Caps and (Hyper)oval

Let b ≥ 3 and C1, C2 be si-caps in the projective space PG(ui, b) for i = 1, 2. Then it is shown in [1, Theorem 9] that an (s0s1s2)-cap in PG(u1 + u2 + 2, b) with s0 = b + 1 if b is odd and s0 = b + 2 if b is even can be constructed.

The new cap is obtained by building the product of C1 and the (hyper-)oval in AG(2, b) (which yields an (s0s1)-cap in the affine space AG(u1 + 2, b)), and then building the product of this cap with C2.

See Also

References

[1]Yves Edel and Jürgen Bierbrauer.
Recursive constructions for large caps.
Bulletin of the Belgian Mathematical Society. Simon Stevin, 6(2):249–258, 1999.
[2]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. “Product of Two Projective Caps and (Hyper)oval.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_CCapProduct2Oval.html

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