Skip to Main Content
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.