A spectral approach to arithmetic correlations for binary FCSR sequences with prime connection integers
Chenhuang Wu
Arithmetic correlation is an important metric for measuring feedback with carry shift register (FCSR) sequences, and its value should be as small as possible. For binary FCSR sequences with a prime connection integer $p$ and for which $\operatorname{ord}_p(2)$ is odd, where $\operatorname{ord}_p(2)$ is the order of $2$ modulo $p$, the arithmetic correlation can be expressed as the difference between the number of even representatives and the number of odd representatives within the subgroup ge