论文标题
弯曲和$ \ Mathbb z_ {2^k} $ - 弯曲的函数类似涂抹分区的函数
Bent and $\mathbb Z_{2^k}$-bent functions from spread-like partitions
论文作者
论文摘要
弯曲的弯曲功能来自向量空间$ v_n $超过$ \ mathbb f_2 $ dimension $ n = 2m $ in Cyclic group $ \ mathbb z_ {2^k} $，或等效地，相对差异集中的相对差异集$ v_n \ times \ times \ times \ mathbb z_ {2^k} $ a $ n MATH con n Math can $ n Math cain bes k z_从任何$ k \ le n/2 $的$ v_n $的差价中。在本文中，弯曲功能的存在和构建从$ v_n $到$ \ m m缩bb z_ {2^k} $，这些功能并非来自扩散构造。从$ v_n $到$ \ mathbb z_ {2^k} $，$ k \ le n/6 $的构造构造从$ \ mathbb f_ {2^m} \ times \ times \ mathbb f_} $ a的分区中获得，$ k \ le n/6 $（更一般而 传播。至于利差，这些分区的一定数量固定数量的结合始终是布尔弯曲函数的支持。
Bent functions from a vector space $V_n$ over $\mathbb F_2$ of even dimension $n=2m$ into the cyclic group $\mathbb Z_{2^k}$, or equivalently, relative difference sets in $V_n\times\mathbb Z_{2^k}$ with forbidden subgroup $\mathbb Z_{2^k}$, can be obtained from spreads of $V_n$ for any $k\le n/2$. In this article, existence and construction of bent functions from $V_n$ to $\mathbb Z_{2^k}$, which do not come from the spread construction is investigated. A construction of bent functions from $V_n$ into $\mathbb Z_{2^k}$, $k\le n/6$, (and more generally, into any abelian group of order $2^k$) is obtained from partitions of $\mathbb F_{2^m}\times\mathbb F_{2^m}$, which can be seen as a generalization of the Desarguesian spread. As for the spreads, the union of a certain fixed number of sets of these partitions is always the support of a Boolean bent function.
