We consider the class of Rudin–Shapiro-like polynomials, whose $L^4$ norms on the complex unit circle were studied by Borwein and Mossinghoff. The polynomial $f(z)=f_0+f_{1}z+\cdots +f_d{z}^d$ is identified with the sequence $(f_0,f_1,\dots ,f_d)$ of its coefficients. From the $L^4$ norm of a polynomial, one can easily calculate the autocorrelation merit factor of its associated sequence, and conversely. In this paper, we study the crosscorrelation properties of pairs of sequences associated to Rudin–Shapiro-like polynomials. We find an explicit formula for the crosscorrelation merit factor. A computer search is then used to find pairs of Rudin–Shapiro-like polynomials whose autocorrelation and crosscorrelation merit factors are simultaneously high. Pursley and Sarwate proved a bound that limits how good this combined autocorrelation and crosscorrelation performance can be. We find infinite families of polynomials whose performance approaches quite close to this fundamental limit.

我们考虑类Rudin–Shapiro的多项式，其 ${\mathrm{大号}}^4$Borwein和Mossinghoff研究了复杂单位圆上的范数。多项式$F（ž）=F_0+F_{\mathrm{1个}}ž+\cdots +F_d{ž}^d$ 用序列识别 $（F_0，F_{\mathrm{1个}}，\dots ，F_d）$其系数。来自${\mathrm{大号}}^4$多项式的范数，可以很容易地计算出其相关序列的自相关优因数，反之亦然。在本文中，我们研究了与Rudin–Shapiro类多项式相关的序列对的互相关特性。我们为互相关优因数找到了一个明确的公式。然后使用计算机搜索来找到对数类似的Rudin–Shapiro多项式，其自相关和互相关优因数同时很高。Pursley和Sarwate证明了一个局限性，它限制了这种自相关和互相关组合性能的好坏。我们发现多项式的多项式的性能接近该基本极限。