Several New Infinite Families of Bent Functions and Their Duals
Several New Infinite Families of Bent Functions and Their Duals
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DOI：
10.1109/tit.2014.2320974
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发表时间：
2014-06
影响因子：
2.5
通讯作者：
Sihem Mesnager
中科院分区：
文献类型：
--
作者：
Sihem Mesnager
Bent函数是最优组合对象。自从它们被引入以来，在过去的三十年里，人们对它们的研究做出了很大的努力。Bent函数的完全分类在今天看来是难以捉摸的，看起来也是没有希望的，因此，不仅它们的表征，而且它们的生成都是具有挑战性的问题。本文致力于Bent函数的构造。首先，我们给出了Bent函数、自对偶Bent函数和反自对偶Bent函数的几种新的有效构造。其次，我们通过显式计算它们的对偶，给出了七个新的Bent函数无限族。
Bent functions are optimal combinatorial objects. Since their introduction, substantial efforts have been directed toward their study in the last three decades. A complete classification of bent functions is elusive and looks hopeless today, therefore, not only their characterization, but also their generation are challenging problems. This paper is devoted to the construction of bent functions. First, we provide several new effective constructions of bent functions, self-dual bent functions, and antiself-dual bent functions. Second, we provide seven new infinite families of bent functions by explicitly calculating their dual.