### 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 F_{M}-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 F_{3}-linear complexities of the ternary Sidel'nikov sequences are determined for p = 2•3^{λ} +1(1 ≤ λ ≤ 20). It turns out that all of the linear complexities of the considered sequences are very close to their periods.

Original language | English |
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Title of host publication | 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 2274-2278 |

Number of pages | 5 |

ISBN (Electronic) | 9781538692912 |

DOIs | |

Publication status | Published - 2019 Jul |

Event | 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France Duration: 2019 Jul 7 → 2019 Jul 12 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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Volume | 2019-July |

ISSN (Print) | 2157-8095 |

### Conference

Conference | 2019 IEEE International Symposium on Information Theory, ISIT 2019 |
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Country | France |

City | Paris |

Period | 19/7/7 → 19/7/12 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

_{M}-linear Complexity of M-ary Sidel'nikov Sequences of Period p - 1 = f • M

^{λ}. 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

}

_{M}-linear Complexity of M-ary Sidel'nikov Sequences of Period p - 1 = f • M

^{λ}. 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 F _{M}-linear Complexity of M-ary Sidel'nikov Sequences of Period p - 1 = f • M^{λ}.** / Zeng, Min; Luo, Yuan; Song, Min Kyu; Song, Hong Yeop.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - The FM-linear Complexity of M-ary Sidel'nikov Sequences of Period p - 1 = f • Mλ

AU - Zeng, Min

AU - Luo, Yuan

AU - Song, Min Kyu

AU - Song, Hong Yeop

PY - 2019/7

Y1 - 2019/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85073168957&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073168957&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2019.8849276

DO - 10.1109/ISIT.2019.8849276

M3 - Conference contribution

AN - SCOPUS:85073168957

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2274

EP - 2278

BT - 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

ER -

_{M}-linear Complexity of M-ary Sidel'nikov Sequences of Period p - 1 = f • M

^{λ}. 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