Binary sequences are characterized by various features. Two of these characteristics—alternation rate and run length—have repeatedly been shown to influence judgments of randomness. The two characteristics, however, have usually been investigated separately, without controlling for the other feature. Because the two features are correlated but not identical, it seems critical to analyze their unique impact, as well as their interaction, so as to understand more clearly what influences judgments of randomness. To this end, two experiments on the perception of binary sequences orthogonally manipulated alternation rate and maximum run length (i.e., length of the longest run within the sequence). Results show that alternation rate consistently exerts a unique effect on judgments of randomness, but that the effect of alternation rate is contingent on the length of the longest run within the sequence. The effect of maximum run length was found to be small and less consistent. Together, these findings extend prior randomness research by integrating literature from the realms of perception, categorization, and prediction, as well as by showing the unique and joint effects of alternation rate and maximum run length on judgments of randomness.

In the area of electromagnetic metrology, binary coded excitation signals become more and more important and various binary coded sequences are available. The measurement approach is to assess the impulse response function of a device under test by correlating the response signal with the excitation signal. In order to achieve a high measurement reproducibility as well as a high dynamic range, the generated binary coded signals have to provide low-noise. In this contribution, a low-noise signal generator realized with a field programmable gate array is presented. The performance investigation of different kinds of binary coded excitation signals and different correlation concepts have been practically investigated. With a chip rate of 5 Gchip/s, the generator can be utilized for ultra-wideband applications. In order to allow for a low-noise and long-term stable signal generation, a new clock generator concept is presented and results of phase noise measurements are shown. Furthermore, an algorithm to fast and precisely shifting the time lag between two binary coded signals for correlating excitation and response signals with a hardware correlator is presented. Finally, the realized demonstrator system is tested using two commonly used types of binary coded sequences.

Let $\text{ }\!\!\lambda\!\!\text{ }\left( n \right)$ denote the Liouville function. Complementary to the prime number theorem, Chowla conjectured that

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$$\sum\limits_{n\le x}{\lambda \,\left( f\left( n \right) \right)}=o\left( x \right)$$

for any polynomial $f\left( x \right)$ with integer coefficients which is not of form $bg{{\left( x \right)}^{2}}$.