Abstract
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. These codes have advantages over conventional Gray codes in certain quantization and coding applications. We survey the main results on this problem, their connections to sequence design, and discuss some of the interesting open problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Etzion, T., Paterson, K.G.: Near optimal single-track Gray codes. IEEE Trans. on Inform. Theory 42, 779–789 (1996)
Gilbert, E.N.: Gray codes and paths on the n-cube. Bell Syst. Tech. Journal 37, 815–826 (1958)
Gray, F.: Pulse codes. US Patent application 237(7), 94–111 (1953)
Hiltgen, A.P., Paterson, K.G., Brandestini, M.: Single-track Gray codes. IEEE Trans. on Inform. Theory 42, 1555–1561 (1996)
Schwartz, M., Etzion, T.: The structure of single-track Gray codes. IEEE Trans. on Inform. Theory 45, 2383–2396 (1999)
Savage, C.: A survey of combinatorial Gray codes. SIAM Reviews 39, 605–629 (1997)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Etzion, T. (2007). Single-Track Gray Codes and Sequences. In: Golomb, S.W., Gong, G., Helleseth, T., Song, HY. (eds) Sequences, Subsequences, and Consequences. Lecture Notes in Computer Science, vol 4893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77404-4_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-77404-4_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77403-7
Online ISBN: 978-3-540-77404-4
eBook Packages: Computer ScienceComputer Science (R0)