Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

On s-uniform property of compressing sequences derived from primitive sequences modulo odd prime powers

模奇素数幂剩余类环上本原序列导出序列的同s分布性质

Abstract

Let Z/(p e) be the integer residue ring modulo p e with p an odd prime and e ≥ 2. We consider the suniform property of compressing sequences derived from primitive sequences over Z/(p e). We give necessary and sufficient conditions for two compressing sequences to be s-uniform with α provided that the compressing map is of the form ϕ(x 0, x 1,...,x e−1) = g(x e−1) + η(x 0, x 1,..., x e−2), where g(x e−1) is a permutation polynomial over Z/(p) and η is an (e − 1)-variable polynomial over Z/(p).

创新点

本文考虑模奇素数幂剩余类环Z/(p)上本原序列压缩导出序列的同分布性质。假定压缩映射形如ϕ(x 0, x 1,...,x e−1) = g(x e−1) + η(x 0, x 1,..., x e−2),并且g(x e−1)是置换多项式。对任意属于Z/(p)的s,我们给出了压缩序列同s分布的等价条件。另外,我们也得到了一个充分条件,在此条件下,对任意属于Z/(p)的k,若两条压缩序列在某特定序列取k值时同s分布,则导出这两条压缩序列的本原序列必相等。

This is a preview of subscription content, log in to check access.

References

  1. 1

    Zheng Q-X, Qi W-F, Tian T. Further result on distribution properties of compressing sequences derived from primitive sequences over Z/(pe). IEEE Trans Inf Theory, 2013, 59: 5016–5022

  2. 2

    Ward M. The arithmetical theory of linear recurring series. Trans Amer Math Soc, 1933, 35: 600–628

  3. 3

    Kurakin V L, Kuzmin A S, Mikhalev A V, et al. Linear recurring sequences over rings and modules. J Math Sci, 1995, 76: 2793–2915

  4. 4

    Huang M Q, Dai Z D. Projective maps of linear recurring sequences with maximal p-adic periods. Fibonacci Quart, 1992, 30: 139–143

  5. 5

    Kuzmin A S, Nechaev A A. Linear recursive sequences over Galois rings. Russ Math Surv, 1993, 48: 171–172

  6. 6

    Tian T, Qi W-F. Injectivity of compressing maps on primitive sequences over Z/(pe). IEEE Trans Inf Theory, 2007, 53: 2960–2966

  7. 7

    Zhu X-Y, Qi W-F. Compression mappings on primitive sequences over Z/(pe). IEEE Trans Inf Theory, 2004, 50: 2442–2448

  8. 8

    Zhu X-Y, Qi W-F. Further result of compressing maps on primitive sequences modulo odd prime powers. IEEE Trans Inf Theory, 2007, 53: 2985–2990

  9. 9

    Zheng Q-X, Qi W-F. Distribution properties of compressing sequences derived from primitive sequences over Z/(pe). IEEE Trans Inf Theory, 2010, 56: 555–563

  10. 10

    Jiang Y P, Lin D D. Distribution properties of compressing sequences derived from primitive sequences modulo odd prime powers. IEEE Trans Inf Theory, 2014, 60: 6602–6608

  11. 11

    Dai Z D. Binary sequences derived from ML-sequences over rings I: periods and minimal polynomials. J Crypt, 1992, 5: 193–207

Download references

Author information

Correspondence to Yupeng Jiang.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Jiang, Y., Zheng, Q. & Lin, D. On s-uniform property of compressing sequences derived from primitive sequences modulo odd prime powers. Sci. China Inf. Sci. 60, 052102 (2017). https://doi.org/10.1007/s11432-015-5472-x

Download citation

Keywords

  • compressing map
  • linear recurring sequence
  • primitive sequence
  • permutation polynomial
  • s-uniform
  • 052102

关键词

  • 压缩映射
  • 线性递归序列
  • 本原序列
  • 置换多项式
  • 同s分布