Finding Non-liner Register on Binary M-Sequence Generating Binary Multiplication Sequence

Updata:01-01-1970

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By:Ahmad Al Cheikha, Diana Mokayes

DOI: https://doi.org/10.30564/ese.v3i2.4036

Abstract:

In the current time there is an important problem that is for a received linear or nonlinear binary sequence {zn} how we can find the nonlinear feedback shift register and its linear equivalent which generate this sequence. The linear orthogonal sequences, special M-Sequences, play a big role in these methods for solving this problem. In the current research trying give illuminations about the methods which are very useful for solving this problem under short sequences, and study these methods for finding the nonlinear feedback shift register of a multiplication sequence and its linear equivalent feedback shift register of a received multiplication binary sequence{zn} where the multiplication on h degrees of a binary linear sequence {an}, or finding the equivalent linear feedback shift register of {zn}, where the sequence {zn}of the form M-sequence, and these methods are very effectively. We can extend these methods for the large sequences using programming and modern computers with large memory.

References:

[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 equences 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(pn) ”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/pmZ.Research Journal of Mathematics and Computer Science. RJMCS.ISSN: 2576-3989, Vol.2, Issue 11. Pp. 0001- 0013. [7] 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. [8] 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. [9] Al Cheikha A. H., Omar Ebtisam. Haj., “Study the Multiplication M-sequences and its Reciprocal Sequences”, Journal of Electronic & Information Sysems. 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:www. researchgate.net/profile/Ahmad_Al_Cheikha/publications After select:Ahmad Al Cheikha | Ahlia University | Department of ... – Research Gate after select: Research, and after select: Article, or Faulltexts, and the article. [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.

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