Title :
Binomial moments of the distance distribution: bounds and applications
Author :
Ashikhmin, A. ; Barg, A.
Author_Institution :
Los Alamos Nat. Lab., NM, USA
Abstract :
We study a combinatorial invariant of codes which counts the number of ordered pairs of codewords in all subcodes of a given support in a code. The main part of this work is related to deriving lower bounds on this invariant, both finite and asymptotic. These bounds are used to obtain new lower bounds on the probability of undetected error of binary codes on the binary symmetric channel (BSC) which improve previously known results. We also derive new asymptotic upper bounds on the exponent of undetected error and extend the region of code rates in which this exponent is tight
Keywords :
binary codes; error statistics; telecommunication channels; asymptotic upper bounds; binary codes; binary symmetric channel; binomial moments; code rates; code support; codewords; combinatorial invariant; distance distribution; finite bound; lower bounds; ordered pairs; subcodes; undetected error exponent; undetected error probability; Binary codes; Decoding; Information theory; Laboratories; Polynomials; Postal services; Reliability theory; Upper bound;
Conference_Titel :
Information Theory, 1998. Proceedings. 1998 IEEE International Symposium on
Conference_Location :
Cambridge, MA
Print_ISBN :
0-7803-5000-6
DOI :
10.1109/ISIT.1998.709042
