Almost Bent functions for Hadamard matrices and APN functions

[EN] It is well-known that bent sequences are linked to Sylvester Hadamard matrices. Recently, the notion of bent sequence has been extended to other kinds of Hadamard matrices. The aim of this paper is not only to review some progresses on bent sequences for Hadamard matrices, but also to suggest an analogous approach for Almost Bent functions. The notion of Almost Bent function attached to a Hadamard matrix is introduced and two open questions in connection with Almost Perfect Nonlinear functions are formulated.