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

Bibliographical note

Funding Information:
This work is supported by National Natural Science Foundation of China under Grant 61871264 and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No.2017R1A2B4011191).

All Science Journal Classification (ASJC) codes

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

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