## Product of Two Projective Caps and (Hyper)oval

Let *b* ≥ 3 and *C*_{1}, *C*_{2} 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 (*s*_{0}*s*_{1}*s*_{2})-cap in PG(*u*_{1} + *u*_{2} + 2, *b*) with *s*_{0} = *b* + 1 if *b* is odd and *s*_{0} = *b* + 2 if *b* is even can be constructed.

The new cap is obtained by building the product of *C*_{1} and the (hyper-)oval in AG(2, *b*) (which yields an (*s*_{0}*s*_{1})-cap in the affine space AG(*u*_{1} + 2, *b*)), and then building the product of this cap with *C*_{2}.

### 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.”
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http://mint.sbg.ac.at/desc_CCapProduct2Oval.html