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Paper 2007/370
FURTHER PROPERTIES OF SEVERAL CLASSES OF BOOLEAN FUNCTIONS WITH OPTIMUM ALGEBRAIC IMMUNITY
Claude Carlet and Xiangyong Zeng and Chunlei Li and Lei Hu
Abstract
Thanks to a method proposed by Carlet, several classes of balanced Boolean functions with optimum algebraic immunity are obtained. By choosing suitable parameters, for even $n\geq 8$, the balanced $n$-variable functions can have nonlinearity $2^{n-1}-{n-1\choose\frac{n}{2}-1}+2{n-2\choose\frac{n}{2}-2}/(n-2)$, and for odd $n$, the functions can have nonlinearity $2^{n-1}-{n-1\choose\frac{n-1}{2}}+\Delta(n)$, where the function $\Delta(n)$ is describled in Theorem 4.4. The algebraic degree of some constructed functions is also discussed.
Metadata
- Available format(s)
- Category
- Foundations
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- boolean functions
- Contact author(s)
- xzeng @ hubu edu cn
- History
- 2007-09-19: received
- Short URL
- https://ia.cr/2007/370
- License
-
CC BY