5. Bent functions🔗

Carlet's Chapter 6 develops the extremal nonlinear Boolean functions in even dimension. Write V_n=\mathbb F_2^n, use the unnormalized Walsh transform W_f, and denote the dual of a bent function f by \widetilde f.

1. 5.1. Bentness
2. 5.2. The dual
3. 5.3. Bent functions of low algebraic degrees
4. 5.4. Bound on algebraic degree
5. 5.5. Primary constructions of bent functions
6. 5.6. Secondary constructions of bent functions
7. 5.7. Decompositions of bent functions
8. 5.8. On the number of bent functions
9. 5.9. Characterization through the NNF
10. 5.10. Geometric characterization
11. 5.11. Characterization by second-order covering sequences
12. 5.12. Hyper-bent functions
13. 5.13. Superclasses of bent functions
14. 5.14. Normal and non-normal bent functions
15. 5.15. Kerdock codes