Permutation codes are a class of structured vector quantizers with a
computationally-simple encoding procedure. Here we provide an extension that
preserves the computational simplicity but yields improved operational
rate--distortion performance. The new class of vector quantizers has a codebook
comprising several permutation codes as subcodes. Methods for designing good
code parameters are given. One method depends on optimizing the rate allocation
in a shape--gain vector quantizer with gain-dependent wrapped spherical shape
codebook.