Cart (Loading....) | Create Account
Close category search window
 

The structure of single-track Gray codes

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Schwartz, M. ; Dept. of Comput. Sci., Technion-Israel Inst. of Technol., Haifa, Israel ; Etzion, T.

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. We investigate the structure of such binary codes and show that there is no such code with 2n codewords when n is a power of 2. This implies that the known codes with 2n-2n codewords. when n is a power of 2, are optimal. This result is then generalized to codes over GF(p), where p is a prime. A subclass of single-track Gray codes, called single-track Gray codes with k-spaced heads, is also defined. All known systematic constructions for single-track Gray codes result in codes from this subclass. We investigate this class and show it has a strong connection with two classes of sequences, the full-order words and the full-order self-dual words. We present an iterative construction for binary single-track Gray codes which are asymptotically optimal if an infinite family of asymptotically optimal seed-codes exists. This construction is based on an effective way to generate a large set of distinct necklaces and a merging method for cyclic Gray codes based on necklaces representatives

Published in:

Information Theory, IEEE Transactions on  (Volume:45 ,  Issue: 7 )

Date of Publication:

Nov 1999

Need Help?


IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.