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Necessary Conditions for the Existence of Regular p -Ary Bent Functions

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3 Author(s)
Jong Yoon Hyun ; Dept. of Math., Ewha Womans Univ., Seoul, South Korea ; Heisook Lee ; Yoonjin Lee

We find some necessary conditions for the existence of regular p-ary bent functions (from Znp to Zp), where p is a prime. In more detail, we show that there is no regular p-ary bent function f in n variables with w(Mf) larger than n/2, and for a given nonnegative integer k, there is no regular p-ary bent function f in n variables with w(Mf)=n/2-k ( n+3/2-k, respectively) for an even n ≥ Np,k (an odd n ≥ Np,k, respectively), where Np,k is some positive integer, which is explicitly determined and the w(Mf) of a p-ary function f is some value related to the power of each monomial of f. For the proof of our main results, we use some properties of regular p-ary bent functions, such as the MacWilliams duality, which is proved to hold for regular p-ary bent functions in this paper.

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Information Theory, IEEE Transactions on  (Volume:60 ,  Issue: 3 )