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Autocorrelation and Linear Complexity of Binary Generalized Cyclotomic Sequences with Period pq

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  • Yan Wang
  • Liantao Yan
  • Qing Tian
  • Liping Ding
  • Tianping Zhang

Abstract

Ding constructed a new cyclotomic class V0 ,V1. Based on it, a construction of generalized cyclotomic binary sequences with period pq is described, and their autocorrelation value, linear complexity, and minimal polynomial are confirmed. The autocorrelation function CSw is 3-level if p≡3mod4, and CSw is 5-level if p≡1mod4. The linear complexity LCS>pq/2 if p≡1 mod 8, p>q+1, or p≡3mod4 or p≡−3mod8. The results show that these sequences have quite good cryptographic properties in the aspect of autocorrelation and linear complexity.

Suggested Citation

  • Yan Wang & Liantao Yan & Qing Tian & Liping Ding & Tianping Zhang, 2021. "Autocorrelation and Linear Complexity of Binary Generalized Cyclotomic Sequences with Period pq," Journal of Mathematics, Hindawi, vol. 2021, pages 1-10, April.
    • Handle: RePEc:hin:jjmath:5535887
    DOI: 10.1155/2021/5535887
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