Abstract:
The technique of error-trapping decoding for algebraic codes is studied in combinatorial terms of covering systems. Letn, k, andtbe positive integers such thatn \geq k \g...Show MoreMetadata
Abstract:
The technique of error-trapping decoding for algebraic codes is studied in combinatorial terms of covering systems. Letn, k, andtbe positive integers such thatn \geq k \geq t > 0. An(n, k,t)-covering system is a pair(X, \beta), whereXis a set of sizenand\betais a collection of subsets ofX, each of sizek, such that for allT \subseteq Xof sizet, there exists at least oneB \in \betawithT\subseteq B. Letb(n, k, t)denote the smallest size of\beta, such that(X, \beta)is an(n, k, t)-covering system. It is shown that the complexity of an error-trapping decoding technique is bounded byb(n, k, t)from below. Two new methods for constructing small(n, k, t)-covering systems, the algorithmic method and the difference family method, are given.
Published in: IEEE Transactions on Information Theory ( Volume: 27, Issue: 5, September 1981)