Compact representation of perceptually relevant parts of multimedia data, referred to as robust hashing or fingerprinting, is often used for efficient retrieval from databases and authentication. In previous work, we introduced a framework for robust hashing which improves the performance of any particular feature extraction method. The hash generation was achieved from a feature vector in three distinct stages, namely: quantization, bit assignment and application of the decoding stage of an error correcting code. Results were obtained for unidimensional quantization and bit assignment, on one code only. In this work, we provide a generalisation of those techniques to higher dimensions. Our framework is analysed under different conditions at each stage. For the quantization, we consider both the case where the codevectors are uniformly and nonuniformly distributed. For multidimensional quantizers, bit assignment to the resulting indexes is a non-trivial task and a number of techniques are evaluated. We show that judicious assignment of binary indices to the codevectors of the quantizer improves the performance of the hashing method. Finally, the robustness provided by a number of different channel codes is evaluated.