Balanced Gray Codes With Flexible Lengths

Robinson and Cohn constructed an (n + 2)-bit balanced Gray code (BGC) of length 2ⁿ⁺² from an n-bit BGC. This letter extends their construction to flexible lengths by selecting a subsequence from transition sequence of an n-bit BGC. For any target length, we first derive the length range of the desired subsequence and the occurrence of each bit position in this subsequence. Then, an (n + 2)-bit balanced Gray code of flexible length can be constructed by selecting a subsequence under the two above constraints.