Study the Linear Equivalent of Nonlinear Sequences over <i>Fp</i> Where p Is Larger Than Two

Diana Mokayes; Ahmad Hamza Al Cheikha

doi:doi:10.11648/j.ijics.20200504.12

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Study the Linear Equivalent of Nonlinear Sequences over Fp Where p Is Larger Than Two

Diana Mokayes, Ahmad Hamza Al Cheikha

Published in International Journal of Information and Communication Sciences (Volume 5, Issue 4)

Received: 25 January 2021 Accepted: 2 February 2021 Published: 10 February 2021

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Abstract

Linear orthogonal binary sequences, special M-Sequences, are used widely in the systems communication channels as in the forward links for mixing the information on connection and as in the backward links of these channels to sift this information which transmitted and the receivers get the information in a correct form In current research trying study the construction of the linear equivalent of a product sequence on two, three, and four degrees over a linear sequences from the field Fp, where p is larger than two, and answering on the request, how is the maximum length of the linear equivalent of a product sequence (on a linear sequence {a_n} over the field Fp), is it less than _rN_h as the binary sequences?, or can reach it ?, or the length is exceed this value _rN_h? And is the product sequences are orthogonal? And we show that in some cases, the maximum length _rN_h for the binary sequences is not correct for the linear sequences in the finite field Fp for p larger than two and the result product sequences are not orthogonal, also trying study the product sequence on two different LFSRs, and how can use one shift feedback shift register LFSR as a monitor register of other p registers. In the current time, I think, there is no coders or decoders using the sequences over finite fields Fp where p is larger than 2 and from this idea this article showing very need for using in the future.

Published in	International Journal of Information and Communication Sciences (Volume 5, Issue 4)
DOI	10.11648/j.ijics.20200504.12
Page(s)	46-68
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Linear Sequences, Finite Field, Linear Feedback Shift Register, Orthogonal Sequences, Linear Equivalent, Complexity

References

[1]	Yang K, Kg Kim y Kumar l. d, (2000), “Quasi–orthogonal Sequences for code –Division Multiple Access Systems, “IEEE Trans. information theory, Vol. 46, No 3, PP 982-993.
[2]	Jong-Seon No, Solomon W. & Golomb, (1998), “Binary Pseudorandom Sequences For period 2ⁿ-1 with Ideal Autocorrelation, “IEEE Trans. Information Theory, Vol. 44 No 2, PP 814-817.
[3]	Golamb S. W. (1976), Shift Register Sequences, San Francisco – Holden Day.
[4]	Lee J. S &Miller L. E, (1998), “CDMA System Engineering Hand Book, “Artech House. Boston, London.
[5]	Yang S. C, “CDMA RF, (1998), System Engineering,” Artech House. Boston- London.
[6]	Mac Wiliams, F. G & Sloane, N. G. A., (2006), “The Theory of Error- Correcting Codes,” North-Holland, Amsterdam.
[7]	Kasami, T. & Tokora, H., (1978), “Teoria Kodirovania,” Mir (Moscow).
[8]	Sloane, N. J. A., (1976), “An Analysis Of The Stricture And Complexity of Nonlinear Binary Sequence Generators,” IEEE Trans. Information Theory Vol. It 22 No 6, PP 732-736.
[9]	Al Cheikha A. H. (May 2014), “ Matrix Representation of Groups in the finite Fields GF(pⁿ),”International Journal of Soft Computing and Engineering, Vol. 4, Issue 2, PP 118-125.
[10]	Lidl, R. & Pilz, G., (1984), “Applied Abstract Algebra,” Springer – Verlage New York, 1984.
[11]	Lidl, R. & Niderreiter, H., (1994), “Introduction to Finite Fields and Their Application, “Cambridge university USA.
[12]	Thomson W. Judson, (2013), “Abstract Algebra: Theory and Applications,” Free Software Foundation.
[13]	Fraleigh, J. B., (1971), “A First course In Abstract Algebra, Fourth printing. Addison- Wesley publishing company USA.
[14]	David, J., (2008), “Introductory Modern Algebra, “Clark University USA.
[15]	Al Cheikha. A. H., (2020), "Study the Linear Equivalent of the Binary Nonlinear Sequences". International Journal of Information and Communication Sciences. Vol. 5, No. 3, 2020, pp. 24-39. doi: 10.11648/j.ijics.20200503.11.

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Diana Mokayes, Ahmad Hamza Al Cheikha. (2021). Study the Linear Equivalent of Nonlinear Sequences over Fp Where p Is Larger Than Two. International Journal of Information and Communication Sciences, 5(4), 46-68. https://doi.org/10.11648/j.ijics.20200504.12

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Diana Mokayes; Ahmad Hamza Al Cheikha. Study the Linear Equivalent of Nonlinear Sequences over Fp Where p Is Larger Than Two. Int. J. Inf. Commun. Sci. 2021, 5(4), 46-68. doi: 10.11648/j.ijics.20200504.12

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AMA Style

Diana Mokayes, Ahmad Hamza Al Cheikha. Study the Linear Equivalent of Nonlinear Sequences over Fp Where p Is Larger Than Two. Int J Inf Commun Sci. 2021;5(4):46-68. doi: 10.11648/j.ijics.20200504.12

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@article{10.11648/j.ijics.20200504.12,
  author = {Diana Mokayes and Ahmad Hamza Al Cheikha},
  title = {Study the Linear Equivalent of Nonlinear Sequences over Fp Where p Is Larger Than Two},
  journal = {International Journal of Information and Communication Sciences},
  volume = {5},
  number = {4},
  pages = {46-68},
  doi = {10.11648/j.ijics.20200504.12},
  url = {https://doi.org/10.11648/j.ijics.20200504.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijics.20200504.12},
  abstract = {Linear orthogonal binary sequences, special M-Sequences, are used widely in the systems communication channels as in the forward links for mixing the information on connection and as in the backward links of these channels to sift this information which transmitted and the receivers get the information in a correct form In current research trying study the construction of the linear equivalent of a product sequence on two, three, and four degrees over a linear sequences from the field Fp, where p is larger than two, and answering on the request, how is the maximum length of the linear equivalent of a product sequence (on a linear sequence {an} over the field Fp), is it less than rNh as the binary sequences?, or can reach it ?, or the length is exceed this value rNh? And is the product sequences are orthogonal? And we show that in some cases, the maximum length rNh for the binary sequences is not correct for the linear sequences in the finite field Fp for p larger than two and the result product sequences are not orthogonal, also trying study the product sequence on two different LFSRs, and how can use one shift feedback shift register LFSR as a monitor register of other p registers. In the current time, I think, there is no coders or decoders using the sequences over finite fields Fp where p is larger than 2 and from this idea this article showing very need for using in the future.},
 year = {2021}
}

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TY  - JOUR
T1  - Study the Linear Equivalent of Nonlinear Sequences over Fp Where p Is Larger Than Two
AU  - Diana Mokayes
AU  - Ahmad Hamza Al Cheikha
Y1  - 2021/02/10
PY  - 2021
N1  - https://doi.org/10.11648/j.ijics.20200504.12
DO  - 10.11648/j.ijics.20200504.12
T2  - International Journal of Information and Communication Sciences
JF  - International Journal of Information and Communication Sciences
JO  - International Journal of Information and Communication Sciences
SP  - 46
EP  - 68
PB  - Science Publishing Group
SN  - 2575-1719
UR  - https://doi.org/10.11648/j.ijics.20200504.12
AB  - Linear orthogonal binary sequences, special M-Sequences, are used widely in the systems communication channels as in the forward links for mixing the information on connection and as in the backward links of these channels to sift this information which transmitted and the receivers get the information in a correct form In current research trying study the construction of the linear equivalent of a product sequence on two, three, and four degrees over a linear sequences from the field Fp, where p is larger than two, and answering on the request, how is the maximum length of the linear equivalent of a product sequence (on a linear sequence {an} over the field Fp), is it less than rNh as the binary sequences?, or can reach it ?, or the length is exceed this value rNh? And is the product sequences are orthogonal? And we show that in some cases, the maximum length rNh for the binary sequences is not correct for the linear sequences in the finite field Fp for p larger than two and the result product sequences are not orthogonal, also trying study the product sequence on two different LFSRs, and how can use one shift feedback shift register LFSR as a monitor register of other p registers. In the current time, I think, there is no coders or decoders using the sequences over finite fields Fp where p is larger than 2 and from this idea this article showing very need for using in the future.
VL  - 5
IS  - 4
ER  -

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Author Information

Diana Mokayes

Department of Mechatronics, College of Mechanical Add Electronical Engineering, Tishreen University, Lattakia, Syria
Ahmad Hamza Al Cheikha

Department of Mathematical Science, College of Arts-science and Education, Ahlia University, Manama, Bahrain

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APA Style

Diana Mokayes, Ahmad Hamza Al Cheikha. (2021). Study the Linear Equivalent of Nonlinear Sequences over Fp Where p Is Larger Than Two. International Journal of Information and Communication Sciences, 5(4), 46-68. https://doi.org/10.11648/j.ijics.20200504.12

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ACS Style

Diana Mokayes; Ahmad Hamza Al Cheikha. Study the Linear Equivalent of Nonlinear Sequences over Fp Where p Is Larger Than Two. Int. J. Inf. Commun. Sci. 2021, 5(4), 46-68. doi: 10.11648/j.ijics.20200504.12

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AMA Style

Diana Mokayes, Ahmad Hamza Al Cheikha. Study the Linear Equivalent of Nonlinear Sequences over Fp Where p Is Larger Than Two. Int J Inf Commun Sci. 2021;5(4):46-68. doi: 10.11648/j.ijics.20200504.12

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@article{10.11648/j.ijics.20200504.12,
  author = {Diana Mokayes and Ahmad Hamza Al Cheikha},
  title = {Study the Linear Equivalent of Nonlinear Sequences over Fp Where p Is Larger Than Two},
  journal = {International Journal of Information and Communication Sciences},
  volume = {5},
  number = {4},
  pages = {46-68},
  doi = {10.11648/j.ijics.20200504.12},
  url = {https://doi.org/10.11648/j.ijics.20200504.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijics.20200504.12},
  abstract = {Linear orthogonal binary sequences, special M-Sequences, are used widely in the systems communication channels as in the forward links for mixing the information on connection and as in the backward links of these channels to sift this information which transmitted and the receivers get the information in a correct form In current research trying study the construction of the linear equivalent of a product sequence on two, three, and four degrees over a linear sequences from the field Fp, where p is larger than two, and answering on the request, how is the maximum length of the linear equivalent of a product sequence (on a linear sequence {an} over the field Fp), is it less than rNh as the binary sequences?, or can reach it ?, or the length is exceed this value rNh? And is the product sequences are orthogonal? And we show that in some cases, the maximum length rNh for the binary sequences is not correct for the linear sequences in the finite field Fp for p larger than two and the result product sequences are not orthogonal, also trying study the product sequence on two different LFSRs, and how can use one shift feedback shift register LFSR as a monitor register of other p registers. In the current time, I think, there is no coders or decoders using the sequences over finite fields Fp where p is larger than 2 and from this idea this article showing very need for using in the future.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Study the Linear Equivalent of Nonlinear Sequences over Fp Where p Is Larger Than Two
AU  - Diana Mokayes
AU  - Ahmad Hamza Al Cheikha
Y1  - 2021/02/10
PY  - 2021
N1  - https://doi.org/10.11648/j.ijics.20200504.12
DO  - 10.11648/j.ijics.20200504.12
T2  - International Journal of Information and Communication Sciences
JF  - International Journal of Information and Communication Sciences
JO  - International Journal of Information and Communication Sciences
SP  - 46
EP  - 68
PB  - Science Publishing Group
SN  - 2575-1719
UR  - https://doi.org/10.11648/j.ijics.20200504.12
AB  - Linear orthogonal binary sequences, special M-Sequences, are used widely in the systems communication channels as in the forward links for mixing the information on connection and as in the backward links of these channels to sift this information which transmitted and the receivers get the information in a correct form In current research trying study the construction of the linear equivalent of a product sequence on two, three, and four degrees over a linear sequences from the field Fp, where p is larger than two, and answering on the request, how is the maximum length of the linear equivalent of a product sequence (on a linear sequence {an} over the field Fp), is it less than rNh as the binary sequences?, or can reach it ?, or the length is exceed this value rNh? And is the product sequences are orthogonal? And we show that in some cases, the maximum length rNh for the binary sequences is not correct for the linear sequences in the finite field Fp for p larger than two and the result product sequences are not orthogonal, also trying study the product sequence on two different LFSRs, and how can use one shift feedback shift register LFSR as a monitor register of other p registers. In the current time, I think, there is no coders or decoders using the sequences over finite fields Fp where p is larger than 2 and from this idea this article showing very need for using in the future.
VL  - 5
IS  - 4
ER  -

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