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A class of balanced binary sequences with optimal autocorrelation properties

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3 Author(s)

The construction of a class of balanced binary sequences with optimal autocorrelation properties is described. Given any odd prime p and any positive integer m , a balanced ( \pm 1) binary sequence of length p^{m} - 1 whose cyclic autocorrelation function c (\tau ) satisfies c (0) = p^{m} - 1 , and, for \tau \neq 0, c (\tau ) = +2 or -2 when (p^{m} - 1)/2 is odd, and c(\tau ) = 0 or -4 when (p^{m} - 1)/2 is even is constructed. Optimality is proved by showing that every balanced binary sequence has at least two distinct out-of-phase correlation values which are at least as large as those obtained here.

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Information Theory, IEEE Transactions on  (Volume:23 ,  Issue: 1 )