Abstract
This paper discusses a simple way of increasing the linear complexity of maximal length q-ary sequences. This is attained by using character substitution tables. The achievable maximum of increase is determined and it is shown that a portion of about 1/e of all substitution tables share this maximum. The mean value and the variance of the linear complexity is derived for the sequence's output by randomly chosen substitutions. The special case of permutations as substitutions are investigated, as well. At the end of the paper we propose an extension of the notion of linear complexity.
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References
Zierler, N., "Linear recurring sequences", J.SIAM, Vol.7, 1959.
Golomb, S. W., Shift-Register Sequences. San Francisco: Holden Day, 1967.
Massey, J.L., "Shift-Register Synthesis and BCH Decoding", IEEE Trans. Inform. Theory, Vol. IT-15, Jan. 1969. 4.
Key, E.L., "An analysis of the structure and complexity of nonlinear binary sequence generators", IEEE Trans. Inform. Theory, IT-22, No. 6., Nov. 1976.
L. Brynielson, "On the Linear Complexity of Combined Shift Register Sequences", Advances in Cryptology — Eurocrypt '85, Lecture Notes in Computer Science, No. 219, Springer, 1985.
Simon, M.K., Omura, J.K., Scholtz, R.A., Levitt, B.K., Spread Spectrum Communications, Vol 1., Ch.5., Computer Science Press, 1985.
Rueppel, R.A., New Approaches to Stream Ciphers. Communication and Control Series of Engineering, Springer Verlag, 1986.
T. Siegenthaler, Methoden für den Entwurf von Stream Cipher-Systemen, Doctoral Thesis, ETH Zürich, 1986
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© 1991 Springer-Verlag Berlin Heidelberg
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Vajda, I., Nemetz, T. (1991). Substitution of characters in q-ary m-sequences. In: Sakata, S. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1990. Lecture Notes in Computer Science, vol 508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54195-0_42
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DOI: https://doi.org/10.1007/3-540-54195-0_42
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Print ISBN: 978-3-540-54195-0
Online ISBN: 978-3-540-47489-0
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