Bounds on Distance Distributions in Codes of Known Size
01 January 2005
We treat the problem of bounding components of the possible distance distributions of codes given the knowledge of their size and, perhaps, minimum distance. Using the Beckner inequality we derive upper bounds on distance distribution components which are sometimes better than earlier known ones obtained with the help of linear programming approach. We use an alternative approach to derive upper bounds on the distance distributions in linear codes. As an application of the suggested estimates we derive a lower 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 a function of the code's size and dual distance as well as a lower bound on the threshold for error probability as a function of the code's size and minimum distance.
