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Status of three classes of sequences

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Abstract

Pseudorandom sequences, sometimes shortened as sequences, have played a key role in the applications of digital communications, cryptography and computer science. This research field is an example of scientific research directly born from the real world applications. Specifically, the research on sequences stems from the application of the sequences generated by maximal length linear feedback shift registers to detect returning signals from Explorer 1, the satellite launched on January 31, 1958 by US, shortly after Sputnik, launched by Soviet Union on October 4, 1957 which is the first satellite in the human being civilization. With more than seven decades of the developments of theory and practice of sequences, this field has evolved to acquire a wide range of the tools and methodologies from extremely deep mathematic fields (comparing with other engineering subjects), such as algebraic geometry, number theory, combinatorics, representation theory, harmonic analysis, to just mention a few. In this survey, we present the current status of the research in sequence design along three different directions, i.e., the sequences with 2-level autocorrelation, the sequence sets with low ambiguity, and Golay complementary sequence sets and complete complementary codes.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Waterloo, Waterloo Ontario, N2L 3G1, Canada

    G. Gong

  2. State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, 710071, China

    Z.L. Wang

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Appendix A: List of Acronyms

Appendix A: List of Acronyms

  • almost perfect nonlinear (APN)

  • authenticated encryption (AE)

  • Butson-type Hadamard (BH)

  • code-division multiple access (CDMA)

  • complementary array set (CAS)

  • complementary sequence set (CSS)

  • complete complementary arrays (CCA)

  • complete complementary codes (CCC)

  • complete mutually orthogonal complementary sets (CMOCS)

  • decimation-Hadamard transform (DHT)

  • discrete Fourier transform (DFT)

  • generalized Boolean function (GBF)

  • generalized Reed-Muller (GRM)

  • Globe Position System (GPS)

  • Golay array pair (GAP)

  • inverse DFT (IDFT)

  • linear feedback shift register (LFSR)

  • millimeter-wave (mm-wave)

  • multi-input multi-output (MIMO)

  • orthogonal frequency division multiplexing (OFDM)

  • orthogonal time frequency space (OTFS)

  • parameter unitary (PU)

  • peak-to-average power ratio (PAPR)

  • peak-to-mean envelope power ratio (PMEPR)

  • quadrature amplitude modulation (QAM)

  • Walsh Hadamard Transform (WHT)

  • Welch-Gong (WG)

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Gong, G., Wang, Z. Status of three classes of sequences. Cryptogr. Commun. 15, 257–308 (2023). https://doi.org/10.1007/s12095-022-00585-4

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  • DOI: https://doi.org/10.1007/s12095-022-00585-4

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