Distribution of Digit Patterns in Multi-Value Sequence over the Odd Characteristic Field

The authors have proposed a multi-value sequence called an NTU sequence which is generated by a trace function and the Legendre symbol over a finite field. Most of the properties for NTU sequence such as period, linear complexity, autocorrelation, and cross-correlation have been theoretically shown in our previous work. However, the distribution of digit patterns, which is one of the most important features for security applications, has not been shown yet. In this paper, the distribution has been formulated with a theoretic proof by focusing on the number of 0's contained in the digit pattern.