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

doi:10.1109/ISIT.2019.8849276

The F_M-linear Complexity of M-ary Sidel'nikov Sequences of Period p - 1 = f • M^λ

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

Department of Electrical and Electronic Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 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 F₃-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
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	https://doi.org/10.1109/ISIT.2019.8849276
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
Volume	2019-July
ISSN (Print)	2157-8095

Conference

Conference	2019 IEEE International Symposium on Information Theory, ISIT 2019
Country	France
City	Paris
Period	19/7/7 → 19/7/12

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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Zeng, M., Luo, Y., Song, M. K., & Song, H. Y. (2019). The F_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

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

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.",

author = "Min Zeng and Yuan Luo and Song, {Min Kyu} and Song, {Hong Yeop}",

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).; 2019 IEEE International Symposium on Information Theory, ISIT 2019 ; Conference date: 07-07-2019 Through 12-07-2019",

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Zeng, M, Luo, Y, Song, MK & Song, HY 2019, The F_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.

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 proceeding › Conference contribution

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Zeng M, Luo Y, Song MK, Song HY. The F_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