Sequences with thirteen-valued cross correlations

Yuehui Cui; Jinquan Luo

Sequences with thirteen-valued cross correlations

信息论 2026-05-20 v1 math.IT

作者: Yuehui Cui , Jinquan Luo

摘要

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.

引用

@article{arxiv.2605.19268,
  title  = {Sequences with thirteen-valued cross correlations},
  author = {Yuehui Cui and Jinquan Luo},
  journal= {arXiv preprint arXiv:2605.19268},
  year   = {2026}
}

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