Abstract
Given α and β as two affine transformations on the ring of integers modulo n, define a binary (α,β)sequence as a sequence S = (x 0 ,x 1 ,…xn_1) that satisfies xa(i) = (-1) ixi and x β(i)= (-1) ix,. The aperiodic autocorrelation function of an (α, β) sequence is shown to satisfy a simple property. In particular, the Barker sequences of odd length are characterized as (α, β) sequences. Further (α, β) sequences of various lengths with small correlation are given.
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References
C.E. Cook and M. BernfieldRadar SignalsNew York: Academic Press, 1967.
R.H. Barker, “Group synchronizing of binary digital systems”, inCommunication TheoryW. Jackson (ed)., pp 273–287, 1953.
J. Storer and R. Turyn, “On binary sequences” inProceedings of the American Mathematical SocietyVol. 12, pp 394–399, 1961.
R. Turyn, “Sequences with small correlations” inError Correcting CodesH. B. Mann (ed)., John Wiley and Sons, 1968.
J.L. Massey and J.J. Uhran, Jr., Final Report for Multi-path Study, published by the Department of Electrical Engineering of the Unversity of Notre Dame, 1969.
S.W. Golomb and R.A. Scholtz, “Generalized Barker sequences”IEEE Trans. on Information TheoryVol. IT-11, No. 4, pp 533–537, 1965.
M.J.E. Golay, “A class of finite binary sequences with alternate auto-correlation values equal to zero”IEEE Trans. on Information TheoryVol. IT-18, No. 3, p 449, 1972.
G.E. SéguinBinary Sequences with Specified Correlation PropertiesPh.D. Dissertation, Department of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana, 1971.
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© 1994 Springer Science+Business Media New York
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Seguin, G., Drolet, G. (1994). Binary Sequences With Small Correlations. In: Blahut, R.E., Costello, D.J., Maurer, U., Mittelholzer, T. (eds) Communications and Cryptography. The Springer International Series in Engineering and Computer Science, vol 276. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2694-0_37
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DOI: https://doi.org/10.1007/978-1-4615-2694-0_37
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