On the Nth maximum order complexity and the expansion complexity of a Rudin-Shapiro-like sequence

Abstract

Based on the parity of the number of occurrences of a pattern 10 as a scattered subsequence in the binary representation of integers, a Rudin-Shapiro-like sequence is defined by Lafrance, Rampersad and Yee. The N th maximum order complexity and the expansion complexity of this Rudin-Shapiro-like sequence are calculated in this paper.

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Correspondence to Xiangyong Zeng.

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The authors are supported by the National Natural Science Foundation of China Grant 61472120. The first author is also supported by China Scholarship Council.

This article is part of the Topical Collection on Special Issue on Sequences and Their Applications

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Sun, Z., Zeng, X. & Lin, D. On the Nth maximum order complexity and the expansion complexity of a Rudin-Shapiro-like sequence. Cryptogr. Commun. 12, 415–426 (2020). https://doi.org/10.1007/s12095-019-00396-0

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Keywords

  • Rudin-Shapiro-like sequence
  • Maximum order complexity
  • Expansion complexity

Mathematics Subject Classification (2010)

  • 11B50
  • 11B85
  • 11K45