Ovoid Cap Is Optimal

For b > 2, the ovoid, a cap with b2 + 1 points in the projective space PG(3, b), is the largest cap that can exist in such a space. Therefore, for every linear orthogonal array OA(b4, s,Fb, 3) / linear [s, s−4, 4]-code over Fb we must have sb2 + 1.

This result is due to [1] for b odd and [2] for b even.

See Also

References

[1]Raj Chandra Bose.
Mathematical theory of the symmetrical factorial design.
Sankhyā, 8:107–166, 1947.
MR0026781 (10,201g)
[2]B. Qvist.
Some remarks concerning curves of the second degree in a finite plane.
Annales Academiæ Scientiarum Fennicæ. Series A1, 134:1–27, 1952.
[3]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. “Ovoid Cap Is Optimal.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_CBoundOvoid.html

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