Generalized Gray codes

A more generalized method is presented to enumerate a sequence of all codewords in the (n,r) Gray code. As a generalization, we refer to a bit as git. When the last codeword differs with the first codeword in exactly one element, then the code is said to be cyclic. An algorithm to generate the (n,r) Gray code is presented. As an example, constructional details of a generalized binary Gray code and a generalized ternary Gray code are considered. The generalized (n,r) Gray code is cyclic.