6 papers
On Known APNs
Valérie Gillot ad Philippe Langevin
We present new invariants, APN-extendibility criterion and a backtracking approach to identify several numerical facts supporting the conjecture that the set of 6-bit \APN function…
Spectral Moment of Order Four and the Uniqueness of the CCZ class of Dublin APN Permutation
Valérie Gillot, Philippe Langevin, Abdoulaye Lo
The note provides new apparoaches and results for the search of 6-bit APN-functions based on the classification of 6-bits Boolean functions.
Normality of 8-Bit Bent Function
Valérie Gillot, Philippe Langevin, Alexandr Polujan
Bent functions are Boolean functions in an even number of variables that are indicators of Hadamard difference sets in elementary abelian 2-groups. A bent function in m variables i…
On the normality of Boolean quartics
Valérie Gillot, Philippe Langevin, Alexandr Polujan
In the BFA 2023 conference paper, A. Polujan, L. Mariot and S. Picek exhibited the first example of a non-normal but weakly normal bent function in dimension 8. In this note, we pr…
Covering radius of RM(4,8)
Valérie Gillot, Philippe Langevin
We propose an effective version of the lift by derivation, an invariant that allows us to provide the classification of B(5,6,8)=RM(6, 8)/RM(4,8). The main consequence is to establ…
Classification of some cosets of Reed-Muller codes
Valérie Gillot, Philippe Langevin
This note presents a descending method that allows us to classify quotients of Reed-Muller codes of lenghth 128 under the action of the affine general linear group.