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We consider signature waveform design for synchronous code division multiplexing in the presence of interference and wireless multipath fading channels. The adaptive real/complex signature that maximizes the signal-to-interference-plus-noise ratio (SINR) at the output of the maximum-SINR filter is the minimum-eigenvalue eigenvector of the disturbance autocovariance matrix. In digital communication systems, the signature alphabet is finite and digital signature optimization is NP-hard. In this paper, first we convert the maximum-SINR objective of adaptive binary signature design into an equivalent minimization problem. Then we present an adaptive binary signature design algorithm based on modified Fincke-Pohst (FP) method that achieves the optimal exhaustive search performance with low complexity. In addition, with the derivation of quaternary-binary equivalence, we extend and propose the optimal adaptive signature design algorithm for quaternary alphabet. Numerical results demonstrate the optimality and complexity reduction of our proposed algorithms.