| Abstrakt: |
We study the essential properties of weakly regular p-ary bent functions of ℓ -form, where a p-ary function is from F p m to F p . We observe that most of studies on a weakly regular p-ary bent function f with f (0) = 0 of ℓ -form always assume the gcd-condition: gcd (ℓ - 1 , p - 1) = 1 . We first show that whenever considering weakly regular p-ary bent functions f with f (0) = 0 of ℓ -form, we can drop the gcd-condition; using the gcd-condition, we also obtain a characterization of a weakly regular bent function of ℓ -form. Furthermore, we find an additional characterization for weakly regular bent functions of ℓ -form; we consider two cases m being even or odd. Let f be a weakly regular bent function of ℓ -form preserving the zero element; then in the case that m is odd, we show that f satisfies gcd (ℓ , p - 1) = 2 . On the other hand, when m is even and f is also non-regular, we show that f satisfies gcd (ℓ , p - 1) = 2 as well. In addition, we present two explicit families of regular bent functions of ℓ -form in terms of the gcd-condition. [ABSTRACT FROM AUTHOR] |
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