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,F_b, 3) / linear [s, s−4, 4]-code over F_b we must have s ≤ b² + 1.

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

See Also

• [3, Theorem 16.54]

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