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 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 | |
| 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 |
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Information Systems
- Modelling and Simulation
- Applied Mathematics
Cite this
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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 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.
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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 -