By Topic

Bounds on distance distributions in codes of known size

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

4 Author(s)
Ashikhmin, A.E. ; Lucent Technol., Bell Labs., Murray Hill, NJ, USA ; Cohen, G.D. ; Krivelevich, M. ; Litsyn, S.N.

We treat the problem of bounding components of the possible distance distributions of codes given the knowledge of their size and possibly minimum distance. Using the Beckner inequality from harmonic analysis, we derive upper bounds on distance distribution components which are sometimes better than earlier ones due to Ashikhmin, Barg, and Litsyn. We use an alternative approach to derive upper bounds on distance distributions in linear codes. As an application of the suggested estimates we get an upper bound on the undetected error probability for an arbitrary code of given size. We also use the new bounds to derive better upper estimates on the covering radius, as well as a lower bound on the error-probability threshold, as a function of the code's size and minimum distance.

Published in:

Information Theory, IEEE Transactions on  (Volume:51 ,  Issue: 1 )