.svg){kind=logo}
SOME METHODS TO DESIGN INTERLEAVED SEQUENCES OVER $\mathbb{F}_2$
Keywords:
interleaved sequence, algorithm, decimation, minimum polynomial, m-sequence, class vector.DOI:
https://doi.org/10.17654/0972555522005Abstract
In this paper, we propose a simple method to build an interleaved sequence on $\mathbb{F}_2$ based on the left-shifted and decimation functions and introduce indexing functions to build such a sequence. Furthermore, we characterize interleaved sequences through some of their properties and the algorithms to generate them.
Received: October 22, 2021
Revised: November 29, 2021
Accepted: December 20, 2021
References
Anne Canteaut, Pascale Charpin and Hans Dobbertin, Binary m-sequences with three-valued crosscorrelation: a proof of Welch’s conjecture, IEEE Trans. Inform. Theory 46 (2000), 4-8.
Sara Díaz Cardell, Amparo Fúster-Sabater and Verónica Requena, Interleaving shifted versions of a PN-sequence, Mathematics 9(6) (2021), 687.
Tony Crilly, Interleaving integer sequences, The Mathematical Gazette 91(520) (2007), 27-33.
Amparo Fúster-Sabater and P. Caballero-Gil, Synthesis of cryptographic interleaved sequences by means of linear cellular automata, Appl. Math. Lett. 22(10) (2009), 1518-1524.
Amparo Fúster-Sabater and Sara D. Cardell, Linear complexity of generalized sequences by comparison of PN-sequences, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales, Serie A. Matemáticas 114(2) (2020), 79.
Jing Jane He, Daniel Panario and Qiang Wang, A family of binary sequences from interleaved construction and their cryptographic properties, Contemporary Mathematics, Gary McGuire, Gary L. Mullen, Daniel Panario and Igor E. Shparlinski, eds., American Mathematical Society, Providence, Rhode Island, Vol. 518, 2010, pp. 209-223.
Tor Helleseth, Correlation of m-sequences and related topics, Sequences and their Applications, Discrete Mathematics and Theoretical Computer Science, C. Ding, T. Helleseth and H. Niederreiter, eds., Springer, London, 1999, pp. 49-66.
Tor Helleseth, Open problems on the cross-correlation of m-sequences, Open Problems in Mathematics and Computational Science, Cetin Kaya Koc, ed., Springer International Publishing, Cham, 2014, pp. 163-179.
Shaoquan Jiang, Zhongduo Dai and Guang Gong, Notes on q-ary interleaved sequences, Chinese Science Bulletin 45(6) (2000), 502-507.
Shaoquan Jiang, Zongduo Dai and Guang Gong, On interleaved sequences over finite fields, Discrete Math. 252 (2002), 161-178.
Ravi Kumar, Manish Purohit, Zoya Svitkina and Erik Vee, Interleaved caching with access graphs, Society for Industrial and Applied Mathematics, Proceedings of the Thirty-First Annual ACM-SIAM Symposium on Discrete Algorithms, SODA’20, Salt Lake City, Utah, 2020, pp. 1846-1858.
Yogesh Kumar and N. Rajesh Pillai, On shift sequences for interleaved construction of signal sets with low correlation, Journal of Discrete Mathematical Sciences and Cryptography 11(3) (2008), 319-331.
Cedric Lauradoux, From Hardware to software synthesis of linear feedback shift registers, 2007 IEEE International Parallel and Distributed Processing Symposium, Long Beach, CA, USA, IEEE, 2007, pp. 1-8.
László Mérai, Harald Niederreiter and Arne Winterhof, Expansion complexity and linear complexity of sequences over finite fields, Cryptography and Communications 9(4) (2017), 501-509.
G. J. Ness and T. Helleseth, Cross correlation of m-sequences of different lengths, IEEE Trans. Inform. Theory 52(4) (2006), 1637-1648.
A. Peinado and A. Fúster-Sabater, Generation of pseudorandom binary sequences by means of linear feedback shift registers (LFSRs) with dynamic feedback, Mathematical and Computer Modelling 57(11) (2013), 2596-2604.
Jian Ren, Design of long period pseudo-random sequences from the addition of m-sequences over EURASIP Journal on Wireless Communications and Networking 2004 (2004), Article Number: 802851.
Zhimin Sun and Arne Winterhof, On the maximum order complexity of the Thue-Morse and Rudin-Shapiro sequence, Uniform Distribution Theory 14 (2019), 33-42.
Xiaohu Tang and Guang Gong, New constructions of binary sequences with optimal autocorrelation value/magnitude, IEEE Trans. Inform. Theory 56(3) (2010), 1278-1286.
Xiaohu Tang and Wai Ho Mow, A new systematic construction of zero correlation zone sequences based on interleaved perfect sequences, IEEE Trans. Inform. Theory 54(12) (2008), 5729-5734.
Tongjiang Yan, Zhixiong Chen and Bao Li, A general construction of binary interleaved sequences of period 4N with optimal autocorrelation, Inform. Sci. 287 (2014), 26-31.
Nam Yul Yu and Guang Gong, New binary sequences with optimal autocorrelation magnitude, IEEE Trans. Inform. Theory 54(10) (2008), 4771-4779.
Lu Zhao, About the linear complexity of quaternary sequences with even length, Cryptography and Communications 12(4) (2020), 725-741.
Downloads
Published
Issue
Section
License
Copyright (c) 2021 Pushpa Publishing House, Prayagraj, India
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________________
Attribution: Credit Pusha Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.
