Placement of M-Sequences over the Field Fp in the Space Rn

Ahmad Hamza Al Cheikha

doi:doi:10.11648/j.ijics.20190401.14

| Peer-Reviewed

Placement of M-Sequences over the Field Fp in the Space Rⁿ

Ahmad Hamza Al Cheikha

Published in International Journal of Information and Communication Sciences (Volume 4, Issue 1)

Received: 9 April 2019 Accepted: 14 May 2019 Published: 12 June 2019

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

Spread spectrum communication systems are widely used today in a variety of applications for different purposes such as access of same radio spectrum by multiple users (multiple access), anti-jamming capability (so that signal transmission cannot be interrupted or blocked by spurious transmission from enemy), interference rejection, secure communications, multi-path protection, etc. Several spreading codes are popular for use in practical spread spectrum systems. one of these important codes is Maximal Sequence (M-sequence) length codes, These are the longest codes that can be generated by a shift register of a specific length, The number of 1-s in the complete sequence and the number of 0-s will differ by one, Further, the auto-correlation of an m-sequence is -1, another interesting property of an M-sequence is that the sequence, when added (modulo-2) with a cyclically shifted version of itself, results in another shifted version of the original sequence. Hence, the M-sequences are also known as, pseudo-noise or PN sequences. Current article study placement M-Sequences over the finite field Fp or Mp-Sequences (where p is a prime number) in the space Rⁿ, these sequences can be generated as a closed set under the addition. These sequences form additive groups with the corresponding null sequence that was generated by the feedback shift registers. Such Mp-Sequences see a great application in the forward links of communication channels. Furthermore, they form coders and decoders that combine the information by p during the connection process with the backward links of these channels. These sequences scrutinize the transmitted information to enable it to reach the receivers in an accurate form. This study has defined eminent surfaces in the vector space ‘R’ having dimensions of ‘n’ as quadratic forms, spheres, and planes that contain these sequences.

Published in	International Journal of Information and Communication Sciences (Volume 4, Issue 1)
DOI	10.11648/j.ijics.20190401.14
Page(s)	24-34
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

M-Sequences, Coefficient of Correlation, Orthogonal Sequences, Additive Group, Code, Field Fp, Space Rⁿ

References

[1]	J. S No, S. W. Golomb, G. Gong, H. K Lee, P. Gaal: Binary Pseudorandom Sequences for Period 2ⁿ -1 with Ideal Autocorrelation, IEEE Trans. Information Theory. 44 (1998), 814-817. Doi: 10.1109/18.661528
[2]	J. S. Byrnes. Instant Walsh Functions, SIAM Rever. 12 (1970), 131. Doi: 10.1137/1012013
[3]	Al Cheikha A. H. (May 5, 2014). Matrix Representation of Groups in the Finite Fields GF (p^n). International Journal of soft Computing and Engineering. IJSCE. Vol. 4, Issue 2, pp. 1-6.
[4]	F. G Mac Wiliams & G. A Sloane. The Theory Of Error- Correcting Codes, North-Holland, Amsterdam. (2006).
[5]	K Yang, Y. K Kim, L. D Kumar. Quasi – orthogonal Sequences for code – Division Multiple Access Systems, IEEE Trans. information theory. 46 (2000), 982-993. Doi: 10.1109/18.841175.
[6]	Lidl, R. Nidereiter H. Introduction to Finite Fields and Their Application, Cambridge University, USA. (1994).
[7]	N. J. A Sloane. An Analysis Of The Stricture and Complexity Of Nonlinear Binary Sequence Generators, IEEE Trans. Information Theory. 22 (1976), 732-736. Doi: 10.1109/tit.1976.1055626.
[8]	C. David. Lay, Linear Algebra and its application, ADDISSON-WESLEY, USA. (1997).
[9]	T. H Kacami. Tokora: Teoria Kodirovania Mir (MOSCOW), (1978).
[10]	J. S Lee & L. E Miller. CDMA System Engineering Hand Book, Artech House. Boston-London. (1998).
[11]	R Lidl & G Pilz. Applied Abstract Algebra, Springer – Verlage New York, (1984).
[12]	T. W Judson. Abstract Algebra: Theory and Applications, Free Software Foundation. (2013).
[13]	J. David. Introductory Modern Algebra, Clark University USA. (2008).
[14]	J. B Fraleigh. A First course In Abstract Algebra, Fourth printing. Addison-Wesley publishing company USA. (1971).
[15]	N. L Braha. The Sequence Space Eq N (M, P, S) And Nk−Lacunary Statistical Convergence, Banach J. Math. Anal. 7 (2013), 88-96. Doi: 10.15352/bjma/1358864550.
[16]	S. G Krantz. On limits of sequences of holomorphic functions, (2010).
[17]	G. B. Thomas & R. L Finny. Calculus and Analytic Geometry, Narson Publish House. (1995).
[18]	Q Zameeruddim & V. K Kahana. Solid Geometry, Vicas Publishing House PVT LTD. (1994).
[19]	A. Ivanyi. Density of safe matrices, Acta Universitatis Sapientiae. 1 (2009), 121-142.
[20]	Al Cheikha. Some Properties of M-Sequences Over Finite Field Fp, International Journal of Computer Engineering& Technology. 5 (2014), 61-72.

Cite This Article

Plain Text BibTeX RIS

APA Style

Ahmad Hamza Al Cheikha. (2019). Placement of M-Sequences over the Field Fp in the Space Rn. International Journal of Information and Communication Sciences, 4(1), 24-34. https://doi.org/10.11648/j.ijics.20190401.14

Copy | Download

ACS Style

Ahmad Hamza Al Cheikha. Placement of M-Sequences over the Field Fp in the Space Rn. Int. J. Inf. Commun. Sci. 2019, 4(1), 24-34. doi: 10.11648/j.ijics.20190401.14

Copy | Download

AMA Style

Ahmad Hamza Al Cheikha. Placement of M-Sequences over the Field Fp in the Space Rn. Int J Inf Commun Sci. 2019;4(1):24-34. doi: 10.11648/j.ijics.20190401.14

Copy | Download

@article{10.11648/j.ijics.20190401.14,
  author = {Ahmad Hamza Al Cheikha},
  title = {Placement of M-Sequences over the Field Fp in the Space Rn},
  journal = {International Journal of Information and Communication Sciences},
  volume = {4},
  number = {1},
  pages = {24-34},
  doi = {10.11648/j.ijics.20190401.14},
  url = {https://doi.org/10.11648/j.ijics.20190401.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijics.20190401.14},
  abstract = {Spread spectrum communication systems are widely used today in a variety of applications for different purposes such as access of same radio spectrum by multiple users (multiple access), anti-jamming capability (so that signal transmission cannot be interrupted or blocked by spurious transmission from enemy), interference rejection, secure communications, multi-path protection, etc. Several spreading codes are popular for use in practical spread spectrum systems. one of these important codes is Maximal Sequence (M-sequence) length codes, These are the longest codes that can be generated by a shift register of a specific length, The number of 1-s in the complete sequence and the number of 0-s will differ by one, Further, the auto-correlation of an m-sequence is -1, another interesting property of an M-sequence is that the sequence, when added (modulo-2) with a cyclically shifted version of itself, results in another shifted version of the original sequence. Hence, the M-sequences are also known as, pseudo-noise or PN sequences. Current article study placement M-Sequences over the finite field Fp or Mp-Sequences (where p is a prime number) in the space Rn, these sequences can be generated as a closed set under the addition. These sequences form additive groups with the corresponding null sequence that was generated by the feedback shift registers. Such Mp-Sequences see a great application in the forward links of communication channels. Furthermore, they form coders and decoders that combine the information by p during the connection process with the backward links of these channels. These sequences scrutinize the transmitted information to enable it to reach the receivers in an accurate form. This study has defined eminent surfaces in the vector space ‘R’ having dimensions of ‘n’ as quadratic forms, spheres, and planes that contain these sequences.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Placement of M-Sequences over the Field Fp in the Space Rn
AU  - Ahmad Hamza Al Cheikha
Y1  - 2019/06/12
PY  - 2019
N1  - https://doi.org/10.11648/j.ijics.20190401.14
DO  - 10.11648/j.ijics.20190401.14
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  - 24
EP  - 34
PB  - Science Publishing Group
SN  - 2575-1719
UR  - https://doi.org/10.11648/j.ijics.20190401.14
AB  - Spread spectrum communication systems are widely used today in a variety of applications for different purposes such as access of same radio spectrum by multiple users (multiple access), anti-jamming capability (so that signal transmission cannot be interrupted or blocked by spurious transmission from enemy), interference rejection, secure communications, multi-path protection, etc. Several spreading codes are popular for use in practical spread spectrum systems. one of these important codes is Maximal Sequence (M-sequence) length codes, These are the longest codes that can be generated by a shift register of a specific length, The number of 1-s in the complete sequence and the number of 0-s will differ by one, Further, the auto-correlation of an m-sequence is -1, another interesting property of an M-sequence is that the sequence, when added (modulo-2) with a cyclically shifted version of itself, results in another shifted version of the original sequence. Hence, the M-sequences are also known as, pseudo-noise or PN sequences. Current article study placement M-Sequences over the finite field Fp or Mp-Sequences (where p is a prime number) in the space Rn, these sequences can be generated as a closed set under the addition. These sequences form additive groups with the corresponding null sequence that was generated by the feedback shift registers. Such Mp-Sequences see a great application in the forward links of communication channels. Furthermore, they form coders and decoders that combine the information by p during the connection process with the backward links of these channels. These sequences scrutinize the transmitted information to enable it to reach the receivers in an accurate form. This study has defined eminent surfaces in the vector space ‘R’ having dimensions of ‘n’ as quadratic forms, spheres, and planes that contain these sequences.
VL  - 4
IS  - 1
ER  -

Copy | Download

Author Information

Ahmad Hamza Al Cheikha

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Ahmad Hamza Al Cheikha. (2019). Placement of M-Sequences over the Field Fp in the Space Rn. International Journal of Information and Communication Sciences, 4(1), 24-34. https://doi.org/10.11648/j.ijics.20190401.14

Copy | Download

ACS Style

Ahmad Hamza Al Cheikha. Placement of M-Sequences over the Field Fp in the Space Rn. Int. J. Inf. Commun. Sci. 2019, 4(1), 24-34. doi: 10.11648/j.ijics.20190401.14

Copy | Download

AMA Style

Ahmad Hamza Al Cheikha. Placement of M-Sequences over the Field Fp in the Space Rn. Int J Inf Commun Sci. 2019;4(1):24-34. doi: 10.11648/j.ijics.20190401.14

Copy | Download

@article{10.11648/j.ijics.20190401.14,
  author = {Ahmad Hamza Al Cheikha},
  title = {Placement of M-Sequences over the Field Fp in the Space Rn},
  journal = {International Journal of Information and Communication Sciences},
  volume = {4},
  number = {1},
  pages = {24-34},
  doi = {10.11648/j.ijics.20190401.14},
  url = {https://doi.org/10.11648/j.ijics.20190401.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijics.20190401.14},
  abstract = {Spread spectrum communication systems are widely used today in a variety of applications for different purposes such as access of same radio spectrum by multiple users (multiple access), anti-jamming capability (so that signal transmission cannot be interrupted or blocked by spurious transmission from enemy), interference rejection, secure communications, multi-path protection, etc. Several spreading codes are popular for use in practical spread spectrum systems. one of these important codes is Maximal Sequence (M-sequence) length codes, These are the longest codes that can be generated by a shift register of a specific length, The number of 1-s in the complete sequence and the number of 0-s will differ by one, Further, the auto-correlation of an m-sequence is -1, another interesting property of an M-sequence is that the sequence, when added (modulo-2) with a cyclically shifted version of itself, results in another shifted version of the original sequence. Hence, the M-sequences are also known as, pseudo-noise or PN sequences. Current article study placement M-Sequences over the finite field Fp or Mp-Sequences (where p is a prime number) in the space Rn, these sequences can be generated as a closed set under the addition. These sequences form additive groups with the corresponding null sequence that was generated by the feedback shift registers. Such Mp-Sequences see a great application in the forward links of communication channels. Furthermore, they form coders and decoders that combine the information by p during the connection process with the backward links of these channels. These sequences scrutinize the transmitted information to enable it to reach the receivers in an accurate form. This study has defined eminent surfaces in the vector space ‘R’ having dimensions of ‘n’ as quadratic forms, spheres, and planes that contain these sequences.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Placement of M-Sequences over the Field Fp in the Space Rn
AU  - Ahmad Hamza Al Cheikha
Y1  - 2019/06/12
PY  - 2019
N1  - https://doi.org/10.11648/j.ijics.20190401.14
DO  - 10.11648/j.ijics.20190401.14
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  - 24
EP  - 34
PB  - Science Publishing Group
SN  - 2575-1719
UR  - https://doi.org/10.11648/j.ijics.20190401.14
AB  - Spread spectrum communication systems are widely used today in a variety of applications for different purposes such as access of same radio spectrum by multiple users (multiple access), anti-jamming capability (so that signal transmission cannot be interrupted or blocked by spurious transmission from enemy), interference rejection, secure communications, multi-path protection, etc. Several spreading codes are popular for use in practical spread spectrum systems. one of these important codes is Maximal Sequence (M-sequence) length codes, These are the longest codes that can be generated by a shift register of a specific length, The number of 1-s in the complete sequence and the number of 0-s will differ by one, Further, the auto-correlation of an m-sequence is -1, another interesting property of an M-sequence is that the sequence, when added (modulo-2) with a cyclically shifted version of itself, results in another shifted version of the original sequence. Hence, the M-sequences are also known as, pseudo-noise or PN sequences. Current article study placement M-Sequences over the finite field Fp or Mp-Sequences (where p is a prime number) in the space Rn, these sequences can be generated as a closed set under the addition. These sequences form additive groups with the corresponding null sequence that was generated by the feedback shift registers. Such Mp-Sequences see a great application in the forward links of communication channels. Furthermore, they form coders and decoders that combine the information by p during the connection process with the backward links of these channels. These sequences scrutinize the transmitted information to enable it to reach the receivers in an accurate form. This study has defined eminent surfaces in the vector space ‘R’ having dimensions of ‘n’ as quadratic forms, spheres, and planes that contain these sequences.
VL  - 4
IS  - 1
ER  -

Copy | Download