Indian Journal of Science and Technology

Open Access Open Access  Restricted Access Subscription Access

Computing and Listing of Number of Possible m-Sequence Generators of Order n


Affiliations
1 Department of Electrical and Computer Engineering, College of Engineering, Sultan Qaboos University, P. O. Box 33, Postal Code 123; Muscat, Oman
2 Department of Electrical and Computer Engineering, College of Engineering, SultanQaboos University, P. O. Box 33, Postal Code 123; Muscat, Oman
 

Design of maximal length sequence (m-sequence) generators of order n has many controlling parameters. In the design process of the generators it is essential to ensure that the generator characteristic polynomial corresponds to a primitive polynomial. The complexity of the search problem of primitive polynomials of order n grows as n increases and hence restricts the listing of all parameters of m-sequence generators of order n. This paper presents a computational procedure to determine the number of possible generators of order n. The paper provides a list of all possible m-sequence generators for up to n = 100.

Keywords

m-Sequence, LFSR, Primitive Polynomial, Prime Factors, Mersenne Numbers, MATLAB
User

  • Ahmad A (2012). Better PN generators for CDMA application – a Verilog-HDL implementation approach, International Journal of Information Engineering (IJIE), vol 2(1), 6–11.

  • Ahmad A, Al-Abri D et al. (2012). Adding pseudo-random test sequence generator in the test simulator for DFT approach, Journal of Computer Technology and Applications (JCTA), vol 3(7), 463–470.

  • Ahmad A, and Hayat L (2011). Selection of polynomials for cyclic redundancy check for the use of high speed embedded – an algorithmic procedure, Transactions on Computers (WSEAS), vol 10(1), 16–20.

  • Ahmad A (2010). A simulation experiment on a built-in self test equipped with pseudorandom test pattern generator and Multi-Input Shift Register (MISR), International Journal of VLSI Design & Communication Systems, vol 1, No. 4, 1–12.

  • Ahmad A, and Al-Balushi J (2009). How to design an effective Serial Input Shift Register (SISR) for data compression process of built-in self-test methodology, Proceedings 4th International Design and Test Workshop (IDT’09) held at King Abdul Aziz City for Science and Technology (KAASAT), Riyadh, Saudi Arabia. 372–379.

  • Al-Naamany A M, and Ahmad A (2003). Development of a strong stream ciphering technique using non-linear fuzzy logic selector, Mobile and Wireless Communications, IFIP —The International Federation for Information Processing, vol 106, 199–206.

  • Ahmad A, Al-Musharafi M J et al. (2002). Design and study of a strong stream crypto-system model for e-commerce, Proceeding ICCC ‘02 Proceedings of the 15th International Conference on Computer Communication, vol 1, 619–630.

  • Jamil T, and Ahmad A (2002). An investigation in to the application of linear feedback shift registers for steganography, Proceedings IEEE SoutheastCon2002, Columbia, SC, USA, 239–244.

  • Ahmad A, Al-Musharafi M J et al. (2001). An NLFSR based sequence generator for stream ciphers, Proceedings (SETA’01) - An International Conference on Sequences & Their Applications, Norway (Bergen), 11–13.

  • Golic J D (2000). Cryptanalysis of three mutually clock-controlled stop/go shift registers, IEEE Transactions on Information Technology, vol 46, No. 3, 1081–1090.

  • Ahmad A (1997). Achievement of higher testability goals through the modification of shift register in LFSR based testing, International Journal of Electronics (UK), vol 82, No. 3, 249–260.

  • Chen H W, Aine C J E et al. (1996). Nonlinear analysis of biological systems using short m-sequences and sparse-simulation techniques, Annals of Biomedical Engineering, vol 24, 513–536.

  • Golomb S W (1982). Shift Register Sequences, Aegean Park Press, Revised Edition.

  • Ahmad A, Nanda N K et al. (1990). Are primitive polynomials always best in signature analysis?, IEEE Design & Test of Computers (USA), vol 7, No. 4, 36–38.

  • Blum L, Blum M et al. (1986). A simple unpredictable pseudo-random number generator, SIAM Journal of Computing, vol 15, No. 2, 364–383.

  • Ahmad A, Nanda N K et al. (1988). A critical role of primitive polynomials in an LFSR based testing technique, IEE Electronics Letters (UK), vol 24(15), 953–955.

  • Ahmad A, Al-Busaidi S S et al. (2013). Study on cyclic cross-correlation behavior of maximal length pseudo-random binary sequences, Indian Journal of Industrial and Applied Mathematics (Taylor & Francis), vol 4(1), 33–43.

  • Ahmad A, and Al-Abri D (2012). Design of a pseudo-random binary code generator via a developed simulation model, International Journal on Information Technology (ACEEE - Journal), vol 2(1), 33–36.

  • Ahmad A (2011). Investigation of some quite interesting divisibility situations in a signature analyzer implementation, Transactions on Circuits and Systems (WSEAS), vol 10 (9), 299–308.

  • Ahmad A (1998). An algorithmic generation of sparse primitive polynomials of order n, International Wireless and Telecommunication Symposium (IWATS’98), Shah Alam (Malaysia).

  • Ahmad A, and Elabdalla A M (1997). An efficient method to determine linear feedback connections in shift registers that generate maximal length pseudo-random up and down binary sequences, Computer & Electrical Engineering (Elsevier), vol 23(1), 33–39.

  • Ahmad A, and Al-Maashri A (2008). Investigating some special sequence length generated through an external exclusive-NOR type LFSRs, International Journal Electrical and Computer Engineering, vol 34(1), 270–280.

  • Ahmad A (2003). Realization of a stream cipher with better security and higher reliability goals, 2nd International Conference on Quality, Reliability and Information Technology - Trends and Future Directions, 18–21, 77–78.

  • Ahmad A, Al-Busaidi S et al. (2003). Measurement techniques of LFSR sequences, Proceedings International Symposium onWireless Systems and Networks (ISWSN’03), King Fahad Univ-ersity of Petroleum - Dahran, Kingdom of Saudi Arabia, 1–5.

  • Ahmad A, Nanda N K et al. (1989). The use of irreducible characteristic polynomials in an LFSR based testing of digital circuits, Proceedings of 4th IEEE International Conference of Region 10 (TENCON-89), 494–496.

  • Ahmad A, Ahmed Al-Mashari et al. (2009). On locking conditions in M-sequence generators for the use in digital watermarking, Proceedings International Conference on Methods and Models in Computer Science (ICM2CS09) held at School of Computer & Systems Sciences, Jawaharlal Nehru University, New Delhi, India, 111–115.

  • Ahmad A, Al-Musharafi M J et al. (2001). Study and implementation of properties of m-sequences in MATLAB-SIMULINK – A pass / fail test tool for designs of random generators, Proceedings IEEE / IEE International Conference on Communication, Computer and Power (ICCCP’01), Oman, 191–196.

  • Ahmad A, Al-Musharafi M J et al. (2002). Study and implementation of properties of m-sequences in MATLAB-SIMULINK – A pass / fail test tool for designs of random generators, Journal of Scientific Research – Science and Technology, vol 7 (part 1), 147–156.

  • Al-Lawati A, and Ahmad A (2004). Realization of a simplified controllability computation procedure – a MATLAB-SIMULINK based tool, Sultan Qaboos University Journal for Scientific Research - Science and Technology, Oman, vol 8, 131–143.

  • Ahmad A, and Ruelens D (2013). Development of digital logic design teaching tool using MATLAB & SIMULINK, IEEE Technology and Engineering Education (ITEE), vol 8, No. 1, 7–12.

  • Ahmad A, Ruelens D et al. (2013). Development of verification tool for minimal Boolean equation, IEEE Technology and Engineering Education (ITEE), vol 8, No. 3.

  • MATLAB: Available from: http://www.mathworks.com/


Abstract Views: 464

PDF Views: 0




  • Computing and Listing of Number of Possible m-Sequence Generators of Order n

Abstract Views: 464  |  PDF Views: 0

Authors

A. Ahmad
Department of Electrical and Computer Engineering, College of Engineering, Sultan Qaboos University, P. O. Box 33, Postal Code 123; Muscat, Oman
S. S. Al-Busaidi
Department of Electrical and Computer Engineering, College of Engineering, Sultan Qaboos University, P. O. Box 33, Postal Code 123; Muscat, Oman
M. Awadalla
Department of Electrical and Computer Engineering, College of Engineering, Sultan Qaboos University, P. O. Box 33, Postal Code 123; Muscat, Oman
M. A. K. Rizvi
Department of Electrical and Computer Engineering, College of Engineering, SultanQaboos University, P. O. Box 33, Postal Code 123; Muscat, Oman
N. Mohanan
Department of Electrical and Computer Engineering, College of Engineering, SultanQaboos University, P. O. Box 33, Postal Code 123; Muscat, Oman

Abstract


Design of maximal length sequence (m-sequence) generators of order n has many controlling parameters. In the design process of the generators it is essential to ensure that the generator characteristic polynomial corresponds to a primitive polynomial. The complexity of the search problem of primitive polynomials of order n grows as n increases and hence restricts the listing of all parameters of m-sequence generators of order n. This paper presents a computational procedure to determine the number of possible generators of order n. The paper provides a list of all possible m-sequence generators for up to n = 100.

Keywords


m-Sequence, LFSR, Primitive Polynomial, Prime Factors, Mersenne Numbers, MATLAB

References





DOI: https://doi.org/10.17485/ijst%2F2013%2Fv6i10%2F38796