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

Holes in Generalized Reed–Muller 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

1 Author(s)
Lovett, S. ; Weizmann Inst. of Sci., Rehovot, Israel

The possible relative weights of codewords of Generalized Reed-Muller codes are studied. Let RMq(r,m) denote the code of polynomials over the finite field Fq in m variables of total degree at most r. The relative weight of a codeword f ¿ RMq(r,m) is the fraction of nonzero entries in f. The possible relative weights are studied, when the field Fq and the degree r are fixed, and the number of variables m tends to infinity. It is proved that the set of possible weights is sparse-for any ¿ which is not rational of the form ¿ = ¿/q k, there exists some ¿ > 0 such that no weights fall in the interval (¿-¿,¿+¿). This demonstrates a new property of the weight distribution of Generalized Reed-Muller codes.

Published in:

Information Theory, IEEE Transactions on  (Volume:56 ,  Issue: 6 )

Date of Publication:

June 2010

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.