A Note on Decoding of Superimposed Codes

A superimposed code with general distance D can be used to construct a non-adaptive pooling design. It can then be used to identify a few unknown positives from a large set of items by associating naturally an outcome vector u. A simple method for decoding the outcome vector u is given whenever there are at most bD−1 2 c errors occuring in the outcome vector u. Moreover, another simple method of detecting whether there is any error occuring in the outcome vector u is also given whenever there are at most D − 1 errors in u. Our method is a generalization of the classical result of W. H. Kautz and R. C. Singleton[Nonadaptive binary superimposed codes, IEEE Trans. Inform. Theory, 10:363-377, 1964].