Editing Gray code (section)

=== Two-dimensional Gray code ===

[[File:16QAM Gray Coded.svg|200px|thumb|right|A Gray-coded constellation diagram for rectangular 16-[[Quadrature amplitude modulation|QAM]]]]

Two-dimensional Gray codes are used in communication to minimize the number of bit errors in [[quadrature amplitude modulation]] (QAM) adjacent points in the [[Constellation diagram|constellation]]. In a typical encoding the horizontal and vertical adjacent constellation points differ by a single bit, and diagonal adjacent points differ by 2 bits.<ref name="Krishna_2008"/>

Two-dimensional Gray codes also have uses in [[location identification]]s schemes, where the code would be applied to area maps such as a [[Mercator projection]] of the earth's surface and an appropriate cyclic two-dimensional distance function such as the [[Mannheim metric]] be used to calculate the distance between two encoded locations, thereby combining the characteristics of the [[Hamming distance]] with the cyclic continuation of a Mercator projection.<ref name="Strang-Dammann-Roeckl-Plass_2009"/>