An arbitrary-location pulse determination algorithm based on multipulse linear prediction coding (MP-LPC) is presented. This algorithm can determine all the amplitudes of the pulses at a time according to given pulse locations without the use of analysis-by-synthesis. This ensures that the pulses are optimal in a least-square sense, providing the theoretical foundation to improve the quality of synthesized speech. A fixed-location pulse linear prediction coding (FLP-LPC) method is proposed based on the arbitrary-location pulse determination algorithm. Simulation of the algorithm in MATLAB showed the superior quality of the speech synthesized using pulses in different locations and processed using the arbitrary-location pulse determination algorithm. The algorithm improved speech quality without affecting coding time, which was approximately 1.5% of the coding time for MP-LPC. Pulse locations in FLP-LPC are fixed and do not need to be transmitted, with only LSF, gain, and 16 pulse amplitudes requiring coding and transmission. FLP-LPC allows the generation of synthesized speech similar to G.729 coded speech at a rate of 2.5 kbps.