Necessary Conditions for the Existence of Regular $p$-Ary Bent Functions
Jong Yoon Hyun, Heisook Lee, Yoonjin Lee · IEEE Transactions on Information Theory · 2014
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,kis 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.