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In this paper, the problem of coherently extending the integration time for the acquisition of new Global Navigation Satellite System (GNSS) signals is addressed. Unlike the acquisition of legacy GNSS signals, the presence of secondary codes allows the polarity of the transmitted signal to change each primary code period. These polarity changes have to be recovered, and symbol combinations have to be tested before extending the coherent integration time. The hierarchical structure imposed by secondary codes and the presence of data/pilot channels are exploited to improve the acquisition process. A new algorithm based on the fast m-sequence and Walsh-Hadamard (WH) transforms is developed and used for efficiently testing all the possible symbol combinations. Secondary code constraints are included to further reduce the computational complexity of enumerating all symbol combinations. The proposed algorithms are analyzed in terms of receiver operating characteristics (ROC), and an approximate expression for the probability of false alarm is derived exploiting results from extreme value theory.