Necessary Conditions for the Existence of Regular <formula formulatype="inline"> <tex Notation="TeX">$p$</tex></formula>-Ary Bent Functions

Abstract

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 &#x2265; N<sub>p,k</sub> (an odd n &#x2265; 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.

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Cite 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} }