Bent functions of maximal degree
Çeşmelioğlu, Ayça and Meidl, Wilfried (2012) Bent functions of maximal degree. IEEE Transactions on Information Theory, 58 (2). pp. 1186-1190. ISSN 0018-9448
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Official URL: http://dx.doi.org/10.1109/TIT.2011.2170053
In this article a technique for constructing p-ary bent functions from plateaued functions is presented. This generalizes earlier techniques of constructing bent from near-bent functions. The Fourier spectrum of quadratic monomials is analysed, examples of quadratic functions with highest possible absolute values in their Fourier spectrum are given. Applying the construction of bent functions to the latter class of functions yields bent functions attaining upper bounds for the algebraic degree when $p=3,5$. Until now no construction of bent functions attaining these bounds was known.
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