Gray Codes for Arbitrary Numeral Systems

Maximilian Spitz 📧

July 11, 2023

Abstract

The original Gray code after Frank Gray, also known as reflected binary code (RBC), is an ordering of the binary numeral system such that two successive values differ only in one bit. We provide a theory for a non-Boolean Gray code, which is a generalisation of the idea for an arbitrary base. Contained is the necessary theoretical environment to express and reason about the respective properties.

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Related publications

  • Sankar, K. J., Pandharipande, V. M., & Moharir, P. S. (n.d.). Generalized gray codes. Proceedings of 2004 International Symposium on Intelligent Signal Processing and Communication Systems, 2004. ISPACS 2004. https://doi.org/10.1109/ispacs.2004.1439140

Session Gray_Codes

Cite

× 
@article{Gray_Codes-AFP,
  author  = {Maximilian Spitz},
  title   = {Gray Codes for Arbitrary Numeral Systems},
  journal = {Archive of Formal Proofs},
  month   = {July},
  year    = {2023},
  note    = {\url{https://isa-afp.org/entries/Gray_Codes.html},
             Formal proof development},
  ISSN    = {2150-914x},
}
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