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We propose in this paper to configure a dual Golay complementary pair of sequences (DGCP) by nesting one Golay complementary pair of sequences (GCP) into the other GCP. We show that the DGCP also has the unique property that the side lobes of the correlation functions are cancelled exactly as the conventional GCP. The DGCP allows the simultaneous use of coded RZ-pulses and coded NRZ-pulses in the pump light of the Brillouin optical time-domain analysis (BOTDA). We call them in this paper coded discrete pulses and coded continuous pulses, respectively. The simultaneous use of both types of coded pulses for the BOTDA makes it possible to employ virtually longer code than the use of only one kind of coded pulses. We theoretically show the dependence of signal-to-noise ratio enhancement (SNRE) on the code length of the DGCP as well as on the code lengths of the GCPs used for the discrete and continuous pulses. Examination of the spatial resolution is also given. Experimental results illustrate the theoretical considerations; about 7 dB of SNRE and 10-cm of spatial resolution are achieved by using DGCP, being in accordance with the theory.