Abstract

Union-free codes and disjunctive codes are two combinatorial structures, which are used in a non-adaptive group testing to find a set of d defective elements among n samples by carrying out the minimal number of tests t. It is known that union-free codes have a larger rate, whereas disjunctive codes provide a more efficient decoding algorithm. In this paper we introduce a new family of codes for a non-adaptive group testing with fast decoding. The rate of these codes is not less than the rate of disjunctive codes, while the decoding algorithm has the same complexity. In addition, we derive a lower bound on the rate of new codes for the case of d = 2 defectives, which is significantly better than the bound for disjunctive codes and almost as good as the bound for union-free codes.

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