 In a typical encoding the horizontal and vertical adjacent constellation points differ by a single bit, and diagonal adjacent points differ by 2 bits.The bijective mapping { 0 ↔ 00, 1 ↔ 01, 2 ↔ 11, 3 ↔ 10 } establishes an isometry between the metric space over the finite field formula_85 with the metric given by the Hamming distance and the metric space over the finite ring formula_86 (the usual modular arithmetic) with the metric given by the Lee distance.The mapping is suitably extended to an isometry of the Hamming spaces formula_87 and formula_88.