A Construction of Weakly and Non-Weakly Regular Bent Functions

Details A Construction of Weakly and Non-Weakly Regular Bent Functions A Construction of Weakly and Non-Weakly Regular Bent Functions

2010-11-29

arxiv.org/abs/1011.6242v1

Mathematics

Combinatorics

Scientific paper

In this article a technique for constructing $p$-ary bent functions from near-bent functions is presented. Two classes of quadratic $p$-ary functions are shown to be near-bent. Applying the construction of bent functions to these classes of near-bent functions yields classes of non-quadratic bent functions. We show that one construction in even dimension yields weakly regular bent functions. For other constructions, we obtain both weakly regular and non-weakly regular bent functions. In particular we present the first known infinite class of non-weakly regular bent functions.

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