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Single-track Gray codes are cyclic Gray codes with codewords of length n, such that all the n tracks which correspond to the n distinct coordinates of the codewords are cyclic shifts of the first track. We investigate the structure of such binary codes and show that there is no such code with 2 n codewords when n is a power of 2. This implies that the known codes with 2 n 0 2n codewords, when n is a power of 2, are optimal. This result is then generalized to codes over GF (p), where p is adoi:10.1109/18.796379 fatcat:ud5m6vcstzf45gkxkijnkaraye