A Readily Implemented Single-Error-Correcting Unit-Distance Counting Code

A new unit-distance counting code (similar to the Gray code but having error-checking properties) that offers distinct advantages in the simplicity of the digital equipment required for encoding and decoding is described. This code has application in several special areas of information processing. It is generated by a particular generalization of the family of Gray codes, which has no error- checking features, but shares with the Gray code a simple conversion relationship to the conventional binary counting code. The new code is derived, and its error-checking and code conversion properties are proven by simple combinatorial arguments. The code has a total of K(m)= 2.2^m/2code words of m digits each (m any even integer). It may be employed for correction of single errors or for the detection of double errors.