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Estimating a channel impulse response using a known aperiodic sequence is considered. The problem can be reduced to minimizing the trace of the inverse of a Toeplitz matrix. An efficient algorithm for computing this trace is developed and optimal binary sequences up to length 32 are found and tabulated. The use of complementary sequences in this context is also investigated. It is shown that the eigenvalues of the autocorrelation matrices of a pair of complementary sequences sum to a known constant.