On constructions of bent, semi-bent and five valued spectrum functions from old bent functions
On constructions of bent, semi-bent and five valued spectrum functions from old bent functions
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DOI：
10.3934/amc.2017026
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发表时间：
2017-05
期刊：
影响因子：
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通讯作者：
Sihem Mesnager;Fengrong Zhang
中科院分区：
文献类型：
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作者：
Sihem Mesnager;Fengrong Zhang
本文介绍了具有多种用途的函数的设计方法，特别是构造小权重线性码的方法。在秘密共享、认证码、关联方案和强正则图等方面具有广泛的应用。我们首先给出了弯曲函数的新的二次构造，推广了著名的Rothaus构造及其对偶函数。从我们的推广中，我们证明了我们能够计算由Rothaus构造的弯曲函数的对偶函数。接下来，我们给出了一种构造半弯曲函数和由弯曲函数构造的几个Walsh变换值函数的新方法。
The paper presents methods for designing functions having many applications in particular to construct linear codes with few weights. The former codes have several applications in secret sharing, authentication codes, association schemes and strongly regular graphs. We firstly provide new secondary constructions of bent functions generalizing the well-known Rothaus' constructions as well as their dual functions. From our generalization, we show that we are able to compute the dual function of a bent function built from Rothaus' construction. Next we present a result leading to a new method for constructing semi-bent functions and few Walsh transform values functions built from bent functions.