Generalization of Multiplication M-Sequences over Fp and Its Reciprocal Sequences

Ahmad Al Cheikha (Assistant Professor at Ahlia University)
Ebtisam Haj Omar (Tishreen Univ, Syria)


Mp-Sequences or M-Sequence over Fp not used so much in current time as binary M-Sequences and it is pending with the difficult to construct there coders and decoders of Mp-Sequences further these reasons there is expensive values to construct them but the progress in the technical methods will be lead to fast using these sequences in different life’s ways, and these sequences give more collection of information and distribution them on the input and output links of the communication channels, building new systems with more complexity, larger period, and security. In current article we will study the construction of the multiplication Mp-Sequence {zn}and its linear equivalent, this sequences are as multiple two sequences, the first sequence{Sn}is an arbitrary Mp-Sequence and the second sequence {ζn} reciprocal sequence of the first sequence {Sn}, length of the sequence {zn}, period, orthogonal and the relations between the coefficients and roots of the characteristic polynomial of f(x) and it’s reciprocal polynomial g(x) and compare these properties with corresponding properties in M-Sequences.


Mp-Sequences; Finite fields; Shift register; Orthogonal; Complexity; Characteristic polynomial; Reciprocal polynomial

Full Text:



[1] 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.

[2] Mac Wiliams, F. G & Sloane,N.G.A., (2006), “The Theory of Error- Correcting Codes,” North- Holland, Amsterdam.

[3] Mokayes D. Al Cheikha A. H., (2021- February) Study the Linear Equivalent of Nonlinear Sequences over Fp Where p is larger than two, International Journal of Information and Communication Sciences, ISSN: 2575-1700, Vol. 5, Issue 4, pp 53-75

[4] Al Cheikha A. H. (September,2014). Some Properties of M-Sequences Over Finite Field Fp. International Journal of Computer Engineering & Technology. IJCET. ISSN 0976-6367(Print),ISSN 0976 - 6375(Online),Vol.5, Issue 9. Pp. 61- 72.

[5] Al Cheikha A. H. (May 2014), “ Matrix Representation of Groups in the finite Fields GF(p n ) ”International Journal of Soft Computing and Engineering, Vol. 4, Issue 2, PP 118-125.

[6] Al Cheikha A. H. (2018).Generation New Binary Sequences using Quotient Ring Z/pm Z. Research Journal of Mathematics and Computer Science. RJMCS. ISSN: 2576 -3989, Vol.2, Issue 11. Pp. 0001- 0013.

[7] Al Cheikha, A. H., (2019), Placement of M-Sequences over the Field Fp in the Space Rn, International Journal of Information and Communication Science, IJICS, ISSN: 2575-1700 (Print); ISSN: 2575-1719 (Online), Vol. 4, No.1, Pp. 24-34.

[8] 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, ISSN:2231- 2307, Vol. 4, Issue 2, pp. 1-6.

[9] Al Cheikha A. H., Omar Ebtisam. Haj., “Study the Multiplication M-sequences and its Reciprocal Sequences”, Journal of Electronic & Information Systems. ISSN: 2661-3204, Vol. 03, Issue. 0, Pp. 13-22.

[10] Al Cheikha, A.H. (April 26, 2014). Matrix Representation of Groups in the Finite Fields GF(2^n). International Journal of Soft Computing and Engineering, IJSCE, ISSN: 2231-2307, Vol. 4, Issue 2. pp. 118-125.

[11] Al Cheikhaa A. H. A Theoretical Study for the Linear Homogenous Orthogonal Recurring Sequences. (5 May, 2004). In Almanara Journal, Alalbayt University, Jordan. No 2, 285/2004. (in Arabic), { In English: publications After select: Ahmad Al Cheikha | Ahlia University | Department of ... – ResearchGate After select: Research, and after select: Article, or Faulltexts, and the article between my items}.

[12] Golamb S. W. (1976), Shift Register Sequences, San Francisco – Holden Day.

[13] Lee J.S &Miller L.E, (1998), ”CDMA System Engineering Hand Book, ”Artech House. Boston, London.

[14] Yang S.C,”CDMA RF , (1998), System Engineering,”Artech House. Boston- London.

[15] Lidl, R.& Pilz, G., (1984), ”Applied Abstract Algebra,” Springer – Verlage New York, 1984.

[16] Lidl, R. & Niderreiter, H., (1994), “Introduction to Finite Fields and Their Application, ” Cambridge university USA.

[17] Thomson W. Judson, (2013), “Abstract Algebra: Theory and Applications,” Free Software Foundation.

[18] Fraleigh, J.B., (1971), “A First course In Abstract Algebra, Fourth printing. Addison-Wesley publishing company USA.



  • There are currently no refbacks.
Copyright © 2021 Author(s)

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.