On the notion of duals of certain almost bent functions
Date:
Middle-European Conference on Applied Theoretical Computer Science
Abstract: We employ two different notions of duals of certain classes of Boolean functions which are used for the purpose of deriving other interesting combinatorial objects from suitable mappings from $GF(2)^n$ $\rightarrow$ $GF(2)^n$. A class of particular interest in this context is almost bent (AB) functions having the property that their (Walsh) spectral characterization possess a desired structure. We give a general result regarding the Gold AB functions, state one conjecture regarding the Welch AB functions and some computational results for the Kasami AB functions. Applying another definition of dual, introduced by Hodžić et al. we provide computational evidence that the duals of Gold AB functions may build a space of bent functions (vectorial bent) though a more rigour theoretical analysis is needed.