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Everything about Bent function
Special type of Boolean function
In the mathematical field of combinatorics, a bent function is a Boolean function that is maximally non-linear; it is as different as possible from the set of all linear and affine functions when measured by Hamming distance between truth tables. Concretely, this means the maximum correlation between the output of the function and a linear function is minimal. In addition, the derivatives of a bent function are balanced Boolean functions, so for any change in the input variables there is a 50 percent chance that the output value will change. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Bent functionA 5-minute orientation
- Skim a recent paper: Efficient Image Encryption Based on New Substitution Box Using DNA Coding and Bent FunctionInfluential work since 2022
- Pick up a classic book: The Primer (The Book of Common Prayer)The most-reprinted book on the subject
- Read the landmark paper: Bent-function sequencesCited 203 times
- Go sideways: Boolean functionA closely related topic
- Go sideways: Balanced Boolean functionA closely related topic
📖 Definitions
Noun A Boolean function f:ℤ2n→ℤ2 whose Walsh transform has constant absolute value.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Bent-function sequences
On Bent and Semi-Bent Quadratic Boolean Functions
Construction of bent functions from near-bent functions
Bent and generalized bent Boolean functions
Enumeration of the bent functions of least deviation from a quadratic bent function
Special bent and near-bent functions
On the dual of a Coulter–Matthews bent function
Bent Partition, Vectorial Dual-Bent Function, and LP-Packing Constructions
🆕 Influential since 2022
Efficient Image Encryption Based on New Substitution Box Using DNA Coding and Bent Function
Bent Partitions, Vectorial Dual-Bent Functions and Partial Difference Sets
Bent pipe flow reconstruction based on improved ultrasound Doppler velocimetry and radial basis function neural network
Bent functions satisfying the dual bent condition and permutations with the $$(\mathcal {A}_m)$$ property
A further study on the construction methods of bent functions and self-dual bent functions based on Rothaus’s bent function
📚 Books worth reading
The Primer (The Book of Common Prayer)Church of England · 1510
La Guia Facil del Sexo for DummiesRuth K. Westheimer, Pierre A. Lehu · 1995
Textbook of drug design and discoveryUlf Madsen, Povl Krogsgaard-Larsen · 2009
Living dinosaursGareth Dyke, Gary W. Kaiser · 2011- 📕The living trust advisorJeffrey L. Condon · 2009
- 📕Debates in family law around the globe at the dawn of the 21st centuryKatharina Boele-Woelki · 2009
Bent FunctionsSihem Mesnager · 2016
Finely harmonic functionsBent Fuglede · 1972
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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