In this paper, a block-constrained trellis coded vector quantization (BC-TCVQ) algorithm is combined with an algebraic codebook to produce an algebraic trellis vector code (ATVC) to be used in ACELP coding. ATVC expands the set of allowed algebraic codebook pulse position, and the trellis branches are labeled with these subsets. The Viterbi algorithm is used to select the excitation codevector. A fast codebook search method using an efficient non-exhaustive search technique is also proposed to reduce the complexity of the ATVC search procedure while maintaining the quality of the reconstructed speech. The ATVC block code is used as the fixed codebook of AMR-NB (12.2kbps), which reduces the computational complexity compared to the conventional algebraic codebook.