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

The MacWilliams-Sloane conjecture on the tightness of the Carlitz-Uchiyama bound and the weights of duals of BCH 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)
Moreno, O. ; Dept. of Math., Puerto Rico Univ., Rio Piedras, Puerto Rico ; Moreno, C.J.

Research Problem 9.5 of MacWilliams and Sloane's book, The Theory of Error Correcting Codes (Amsterdam: North-Holland, 1977), asks for an improvement of the minimum distance bound of the duals of BCH codes, defined over F2m with m odd. The objective of the present article is to give a solution to the above problem by with (i) obtaining an improvement to the Ax (1964) theorem, which we prove is the best possible for many classes of examples; (ii) establishing a sharp estimate for the relevant exponential sums, which implies a very good improvement for the minimum distance bounds; (iii) providing a doubly infinite family of counterexamples to Problem 9.5 where both the designed distance and the length increase independently; (iv) verifying that our bound is tight for some of the counterexamples; and (v) in the case of even m, giving a doubly infinite family of examples where the Carlitz-Uchiyama bound is tight, and in this way determining the exact minimum distance of the duals of the corresponding BCH codes

Published in:

Information Theory, IEEE Transactions on  (Volume:40 ,  Issue: 6 )

Date of Publication:

Nov 1994

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.