A general framework for secondary constructions of bent and plateaued functions

New Secondary Constructions of Generalized Bent Functions

“…Example 1 Let q = 8 and m be odd. The function φ(x) ∈ GB 8 m is given by φ(x) = a 0 (x) + 2a 1 (x) + 4a 2 (x)…”

“…The former is also called primary construction, which contains Maiorana-McFarland (M-M) class, Partial spreads (PS) class and Dobbertin's H class (which includes M-M class and a part of PS class) [4] . The latter is also called secondary construction (using known bent functions to built new bent functions), which contains "Rothaus construction [5,6] , direct sum and indirect sum [7,8] ". It is an efficient way to generate more bent functions and thus has received sustained attentions by the researchers in the last decades [9][10][11][12][13][14] .…”

Characterization of Basic 5-Value Spectrum Functions Through Walsh-Hadamard Transform

“…Moreover, considering the design of basic 5-value spectra functions, we provide an efficient and general construction method (Proposition IV.2) which utilizes the spectral construction method introduced in [13]. It is worth noticing that this method addresses any parity of n compared to the approach taken in [15] which only covers even n. For basic 5-value spectrum functions, we show that the two associated dual functions are necessarily plateaued.…”

“…Their various design methods have been addressed in several papers [6], [8], [10], [17], [18], [26], [27]. Due to their simple characterization in the spectral domain an alternative design approach was proposed recently in [13], [14].…”

“…In the second part of this work (Section V), we investigate the equivalence of duals which are obtained by imposing different orderings (in terms of Lemma III.1-(i)) on the affine/linear Walsh-Hadamard support (say) S g of a given basic plateaued function g. Note that this has been left as an open problem in [13], [14]. It is shown that representing S g differently either as…”