A Note on Decoding of Superimposed Codes

AbstractA 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 $$\frac{{D - 1}}{2}$$ 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 Kautz and Singleton (Nonadaptive binary superimposed codes, IEEE Trans. Inform. Theory, vol. 10, pp. 363–377, 1964).