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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© 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
Publisher Name: Springer, Boston, MA
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