Abstract
In [6] and [10], a construction of binary sequences with an (almost) optimal autocorrelation spectrum is suggested. We continue the study of the linear complexity and the linear feedback polynomial of these sequences over \( \mathbb{F} \) 2, originated in [4].
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B. C. Berndt, R. J. Evans and K. S. Williams, Gauss and Jacobi sums, John Wiley & Sons Inc., New York (1998).
T. Beth, D. Jungnickel and H. Lenz, Design Theory, 2nd ed., Cambridge University Press, Cambridge, Vol. 1 (1999).
T. W. Cusick, C. Ding and A. Renvall, Stream Ciphers and Number Theory, North-Holland Publishing Co., Amsterdam (1998).
T. Helleseth and K. Yang, On binary sequences of period n = p m − 1 with optimal autocorrelation, In (T. Helleseth, P. Kumar and K. Yang, eds.), Proceedings of SETA01, (2002) pp. 209–217.
D. Jungnickel and A. Pott, Perfect and almost perfect sequences, Discrete Applied Mathematics, Vol. 95 (1999) pp. 331–359.
A. Lempel, M. Cohn and W. L. Eastman, A class of balanced binary sequences with optimal autocorrelation properties, IEEE Transactions on Information Theory, Vol. 23 (1977) pp. 38–42.
R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia of Mathematics and Its Applications, 2nd ed., Cambridge University Press, Vol. 20 (1997).
A. Pott, Finite Geometry and Character Theory, Lecture Notes in Mathematics, Springer-Verlag, Berlin, Heidelberg, Vol. 1601 (1995).
B. Schmidt, Cyclotomic integers and finite geometry, J. Am. Math. Soc., Vol. 12 (1999) pp. 929–952, to appear.
V. M. Sidel'nikov, Some k-valued pseudo-random sequences and nearly equidistant codes, Problemy Peredačci Informacii, Vol. 5 (1969) pp. 16–22.
T. Storer, Cyclotomy and Difference Sets, Markham Publishing Co., Chicago, Ill. (1967).
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Kyureghyan, G.M., Pott, A. On the Linear Complexity of the Sidelnikov-Lempel-Cohn-Eastman Sequences. Designs, Codes and Cryptography 29, 149–164 (2003). https://doi.org/10.1023/A:1024156525801
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DOI: https://doi.org/10.1023/A:1024156525801