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Some Notes on Prime-Square Sequences

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Abstract

The well-known binary Legendre sequences possess good autocorrelation functions and high linear complexity, and are just special cases of much larger families of cyclotomic sequences. Prime-square sequences are the generalization of these Legendre sequences, but the ratio of the linear complexity to the least period of these sequences approximates to zero if the prime is infinite. However, a relatively straightforward modification can radically improve this situation. The structure and properties, including linear complexity, minimal polynomial, and autocorrelation function, of these modified prime-square sequences are investigated. The hardware implementation is also considered.

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Author information

Authors and Affiliations

  1. School of Information Science and Technology, Donghua University, Shanghai, 201620, China

    En-Jian Bai

  2. State Key Laboratory of Information Security, Graduate University of Chinese Academy of Sciences, Beijing, 100039, China

    En-Jian Bai

  3. Department of Information and Computing Science, Shanghai University of Electric Power, Shanghai, 200090, China

    Xiao-Juan Liu

Authors
  1. En-Jian Bai
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  2. Xiao-Juan Liu
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Corresponding author

Correspondence to En-Jian Bai.

Additional information

This work is supported by the National Natural Science Foundation of China under Grant No. 60503009.

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Bai, EJ., Liu, XJ. Some Notes on Prime-Square Sequences. J Comput Sci Technol 22, 481–486 (2007). https://doi.org/10.1007/s11390-007-9042-6

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  • DOI: https://doi.org/10.1007/s11390-007-9042-6

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