A Recursive Bound on the Size of Affine Caps by Bierbrauer and Edel

Let Cu(b) denote the size of the largest caps in the affine space AG(u, b). Upper bounds on Cu(b) can be obtained by using the recursive formula

Cu(b) ≤ bu – $\displaystyle {\frac{{b^{u}−1}}{{1+b^{1-u}C_{u−1}(b)}}}$

from [1, Theorem 2]. The special case for odd b can already be derived from [2].

See Also

References

[1]Jürgen Bierbrauer and Yves Edel.
Bounds on affine caps.
Journal of Combinatorial Designs, 10(2):111–115, 2002.
doi:10.1002/jcd.10000
[2]Roy Meshulam.
On subsets of finite abelian groups with no 3-term arithmetic progressions.
Journal of Combinatorial Theory, Series A, 71(1):168–172, July 1995.
doi:10.1016/0097-3165(95)90024-1
[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. “A Recursive Bound on the Size of Affine Caps by Bierbrauer and Edel.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. http://mint.sbg.ac.at/desc_ARecursion.html

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