Generalized product code (GPC) vector quantization (VQ) is applied to the coding of speech linear prediction filter parameters. We show that the performance of conventional product code VQ can be improved through the use of conditional feature codebooks and multiple-survivor encoding search. Two particular product code structures, split VQ (SVQ) and multistage VQ (MSVQ), are explored within the GPC framework for the quantization of prediction filter parameters in the line spectral frequency (LSF) domain. Our experiments show that with a suitable MSVQ scheme, 21 bits/frame suffice to encode the LSF parameters to furnish transparent-coding quality. Transparent coding with SVQ requires 22 bits/frame, but only half of the encoding complexity of the best MS VQ scheme.