DocumentCode :
933655
Title :
(n,k,t))-covering systems and error-trapping decoding (Corresp.)
Author :
Chan, Agnes Hui ; Games, Richard A.
Volume :
27
Issue :
5
fYear :
1981
fDate :
9/1/1981 12:00:00 AM
Firstpage :
643
Lastpage :
646
Abstract :
The technique of error-trapping decoding for algebraic codes is studied in combinatorial terms of covering systems. Let 
, and 
be positive integers such that 
. An 
-covering system is a pair 
, where 
is a set of size 
and 
is a collection of subsets of , each of size 
, such that for all 
of size , there exists at least one 
with 
. Let 
denote the smallest size of , such that is an 
-covering system. It is shown that the complexity of an error-trapping decoding technique is bounded by from below. Two new methods for constructing small -covering systems, the algorithmic method and the difference family method, are given.
, and be positive integers such that . An -covering system is a pair , where is a set of size and is a collection of subsets of , each of size , such that for all of size , there exists at least one with . Let denote the smallest size of , such that is an -covering system. It is shown that the complexity of an error-trapping decoding technique is bounded by from below. Two new methods for constructing small -covering systems, the algorithmic method and the difference family method, are given.Keywords :
Decoding; Error-detecting codes; Adders; Decoding; Error correction; Error correction codes; Hardware; Linear code; Logic circuits; Mathematics; Reed-Solomon codes; Research and development;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1981.1056392
Filename :
1056392
Link To Document :
