论文标题
具有良好家庭复杂性和互相关措施的序列家庭
Families of sequences with good family complexity and cross-correlation measure
论文作者
论文摘要
在本文中，我们根据两种措施，家庭复杂性（$ f $ - 复杂性）和订单$ \ ell $的互相关度量来研究一个序列家庭的伪随身。我们不仅在二进制字母上考虑序列，还考虑$ k $ -symbols（$ k $ - ary）字母的序列。我们首先概括了一些有关二元假序列序列的构建的已知方法。我们证明了$ f $ complexity的二进制序列的二进制序列，这些二进制序列是某些不可约多项式的Legendre-Symbols。我们表明，这个家庭及其双重家庭既具有巨大的家庭复杂性，又具有小的互相关度量，直到相当大。接下来，我们介绍另一个具有高$ f $ complexity和低互相关度量的二进制序列系列。然后，我们将结果扩展到$ k $ -Symbols字母的序列家族。
In this paper we study pseudorandomness of a family of sequences in terms of two measures, the family complexity ($f$-complexity) and the cross-correlation measure of order $\ell$. We consider sequences not only on binary alphabet but also on $k$-symbols ($k$-ary) alphabet. We first generalize some known methods on construction of the family of binary pseudorandom sequences. We prove a bound on the $f$-complexity of a large family of binary sequences of Legendre-symbols of certain irreducible polynomials. We show that this family as well as its dual family have both a large family complexity and a small cross-correlation measure up to a rather large order. Next, we present another family of binary sequences having high $f$-complexity and low cross-correlation measure. Then we extend the results to the family of sequences on $k$-symbols alphabet.
