具有良好族复杂度与互相关测度的序列族
Families of sequences with good family complexity and cross-correlation measure
AI总结：
本文研究二元及k元序列族的伪随机性，通过推广构造方法，证明基于不可约多项式Legendre符号的序列族及其对偶族具有高族复杂度和低互相关测度，并进一步构造新的二元序列族并将结果推广到k元情形。
摘要：
本文从两个度量角度研究一族序列的伪随机性：族复杂度（f-复杂度）和ℓ阶互相关测度。我们不仅考虑二元字母表上的序列，还考虑k元（k-ary）字母表上的序列。我们首先推广了一些构造二元伪随机序列族的已知方法。我们证明了一大类由某些不可约多项式的Legendre符号构成的二元序列族的f-复杂度上界。我们证明该族及其对偶族都具有较大的族复杂度和较小的互相关测度，且可达到相当大的阶数。接着，我们提出另一个具有高f-复杂度和低互相关测度的二元序列族。然后我们将这些结果推广到k元字母表上的序列族。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
