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We consider the problem of designing binary spreading sequences in code-division multiplexing (CDM) systems. Our objective is to find the binary spreading sequence that maximizes the pre-detection signal-to-interference-plus-noise (SINR) at the output of maximum-SINR (MSINR) linear filter. However, the maximization problem over the binary field is NP-hard with complexity exponential in the sequence length. In this paper, we present a semidefinite-relaxation-based algorithm with a polynomial computational complexity that outputs the desirable binary solution with the deterministic SINR performance guarantee. Simulation studies demonstrate performance improvement over other known binary sequence assignment algorithms.