The FM-linear Complexity of M-ary Sidel'nikov Sequences of Period p - 1 = f • Mλ

Min Zeng, Yuan Luo, Min Kyu Song, Hong Yeop Song

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The linear complexity is a measure for the unpredictability of a sequence over a finite field. Sequences with good pseudo-random properties and large linear complexity are widely used in the CDMA spread spectrum communication and cryptography. In recent years, many researchers have focused on the linear complexity of cyclotomic sequences such as Sidel'nikov sequence. This paper studies the FM-linear complexity of M-ary Sidel'nikov sequence of period p-1 using the Hasse derivative of its generating function, where M|(p-1). The tth Hasse derivative formulas are generalized in terms of cyclotomic numbers, and then the exact F3-linear complexities of the ternary Sidel'nikov sequences are determined for p = 2•3λ +1(1 ≤ λ ≤ 20). It turns out that all of the linear complexities of the considered sequences are very close to their periods.

Original languageEnglish
Title of host publication2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2274-2278
Number of pages5
ISBN (Electronic)9781538692912
DOIs
Publication statusPublished - 2019 Jul
Event2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France
Duration: 2019 Jul 72019 Jul 12

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2019-July
ISSN (Print)2157-8095

Conference

Conference2019 IEEE International Symposium on Information Theory, ISIT 2019
CountryFrance
CityParis
Period19/7/719/7/12

Fingerprint

Linear Complexity
Derivatives
Spread spectrum communication
Code division multiple access
Cryptography
Cyclotomic numbers
Spread Spectrum Communication
Derivative
Cyclotomic
Code Division multiple Access
Ternary
Generating Function
Galois field

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modelling and Simulation
  • Applied Mathematics

Cite this

Zeng, M., Luo, Y., Song, M. K., & Song, H. Y. (2019). The FM-linear Complexity of M-ary Sidel'nikov Sequences of Period p - 1 = f • Mλ. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings (pp. 2274-2278). [8849276] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2019.8849276
Zeng, Min ; Luo, Yuan ; Song, Min Kyu ; Song, Hong Yeop. / The FM-linear Complexity of M-ary Sidel'nikov Sequences of Period p - 1 = f • Mλ. 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 2274-2278 (IEEE International Symposium on Information Theory - Proceedings).
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abstract = "The linear complexity is a measure for the unpredictability of a sequence over a finite field. Sequences with good pseudo-random properties and large linear complexity are widely used in the CDMA spread spectrum communication and cryptography. In recent years, many researchers have focused on the linear complexity of cyclotomic sequences such as Sidel'nikov sequence. This paper studies the FM-linear complexity of M-ary Sidel'nikov sequence of period p-1 using the Hasse derivative of its generating function, where M|(p-1). The tth Hasse derivative formulas are generalized in terms of cyclotomic numbers, and then the exact F3-linear complexities of the ternary Sidel'nikov sequences are determined for p = 2•3λ +1(1 ≤ λ ≤ 20). It turns out that all of the linear complexities of the considered sequences are very close to their periods.",
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Zeng, M, Luo, Y, Song, MK & Song, HY 2019, The FM-linear Complexity of M-ary Sidel'nikov Sequences of Period p - 1 = f • Mλ. in 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings., 8849276, IEEE International Symposium on Information Theory - Proceedings, vol. 2019-July, Institute of Electrical and Electronics Engineers Inc., pp. 2274-2278, 2019 IEEE International Symposium on Information Theory, ISIT 2019, Paris, France, 19/7/7. https://doi.org/10.1109/ISIT.2019.8849276

The FM-linear Complexity of M-ary Sidel'nikov Sequences of Period p - 1 = f • Mλ. / Zeng, Min; Luo, Yuan; Song, Min Kyu; Song, Hong Yeop.

2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. p. 2274-2278 8849276 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Zeng M, Luo Y, Song MK, Song HY. The FM-linear Complexity of M-ary Sidel'nikov Sequences of Period p - 1 = f • Mλ. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2019. p. 2274-2278. 8849276. (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2019.8849276