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The acquisition of spreading sequences is a crucial task in spread-spectrum communication and ranging receivers. An acquisition method by utilising a multi-bit local code to acquire spread-spectrum signals is presented. The local code design problem towards multiple-support, bounded sidelobe, bounded cross-correlation, balance and bounded variance is formulated and solved through a quadratic programming. Based on the local codes, a multi-layer acquisition approach is devised to yield an overall improvement in acquisition speed. The performance tradeoffs in the code design stage and code acquisition stage are described. Applications of the proposed method to acquire global positioning system and Galileo codes are provided. It is shown that the proposed scheme can effectively reduce the mean acquisition time in comparison with the traditional search approach.