Sequences with thirteen-valued cross correlations
This provides a complete theoretical result for a class of sequences, advancing the understanding of cross-correlation in coding theory and communications.
The paper determines the cross-correlation distribution between an m-sequence and its d-decimated sequence for a specific d, showing it is 13-valued, which is the first time such a distribution has been fully characterized.
In this paper, we completely determine the cross correlation distribution between an $m$-sequence $(s_t)$ of period $p^n-1$ and its $d$-decimated sequence $(s_{dt})$, where $d = \frac{p^n-1}{3} + p^i$, $p \equiv 1 \pmod{3}$, $\frac{1}{3}p^{-i}(p^n-1) \not\equiv 2 \pmod{3}$, and $0 \leq i < n$. It is shown that the cross correlation is $13$-valued. To the best of our knowledge, this is the first time that the cross correlation distribution of so many values has been determined.