Presented here are techniques for generating desired gray codes with properties different from those of the standard binary reflected gray code. For communications using phase shift-keyed (PSK) signals with different significances for different phases, it is desirable to have such codes with different bit error probabilities. For some applications, it is important to have codes with arbitrary crossover Hamming distances. These techniques are suitable for generating codes with either or both of these properties. The codes generated may be far longer than those generated by current computer search techniques.