Product of Two Projective Caps and (Hyper)oval

Let b ≥ 3 and C₁, C₂ be s_i-caps in the projective space PG(u_i, 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

• [2, Theorem 16.62]

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: 2024-09-05. http://mint.sbg.ac.at/desc_CCapProduct2Oval.html