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On a general class of quadratic hopping sequences

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Abstract

Based upon quadratic polynomials over the finite field, a new class of frequency hopping sequences with large family size suitable for applications in time/frequency hopping CDMA systems, multi-user radar and sonar systems is proposed and investigated. It is shown that the new time/frequency hopping sequences have at most one hit in their autocorrelation functions and at most two hits in their crosscorrelation functions except for a special case, and their family size is much larger than the conventional quadratic hopping sequences. The percentage of full collisions for the new quadratic hopping sequences is discussed. In addition, the average number of hits for the new quadratic hopping sequences, quadratic congruence sequences, extended quadratic congruence sequences and the general linear hopping sequences are also derived.

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Authors and Affiliations

  1. School of Economics Information Engineering, Southwestern University of Finance and Economics, Chengdu, 610074, China

    HuaDing Jia

  2. College of Computer Science, Sichuan University, Chengdu, 610064, China

    HuaDing Jia

  3. School of Computer Science, Sichuan Normal University, Chengdu, 610068, China

    Ding Yuan

  4. School of Information Science and Technology, Southwest Jiaotong University, Chengdu, 610031, China

    DaiYuan Peng & Ling Guo

Authors
  1. HuaDing Jia
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  2. Ding Yuan
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  3. DaiYuan Peng
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  4. Ling Guo
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Corresponding author

Correspondence to DaiYuan Peng.

Additional information

Supported by the Scientific Research Fund of Southwestern University of Finance and Economics and the National Natural Science Foundation of China (Grant No. 60572142)

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Jia, H., Yuan, D., Peng, D. et al. On a general class of quadratic hopping sequences. Sci. China Ser. F-Inf. Sci. 51, 2101–2114 (2008). https://doi.org/10.1007/s11432-008-0136-8

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  • DOI: https://doi.org/10.1007/s11432-008-0136-8

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