- Published 2014 in IEEE Transactions on Information Theory

We find some necessary conditions for the existence of regular p-ary bent functions (from Z<sup>n</sup>p 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(M<sub>f</sub>) 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(M<sub>f</sub>)=n/2-k ( n+3/2-k, respectively) for an even n ≥ N<sub>p,k</sub> (an odd n ≥ N<sub>p,k</sub>, respectively), where N<sub>p,k</sub> is some positive integer, which is explicitly determined and the w(M<sub>f</sub>) 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.

@article{Hyun2014NecessaryCF,
title={Necessary Conditions for the Existence of Regular \$p\$ -Ary Bent Functions},
author={Jong Yoon Hyun and Heisook Lee and Yoonjin Lee},
journal={IEEE Transactions on Information Theory},
year={2014},
volume={60},
pages={1665-1672}
}