A fundamental problem in microarray analysis is to identify relevant genes from large amounts of expression data. Feature selection aims at identifying a subset of features for building robust learning models. However, finding the optimal number of features is a challenging problem, as it is a trade off between information loss when pruning excessively and noise increase when pruning is too weak. This paper presents a novel representation of genes as strings of bits and a method which automatically selects the minimum number of genes to reach a good classification accuracy on the training set. Our method first eliminates redundant features, which do not add further information for classification, then it exploits a set covering algorithm. Preliminary experimental results on public datasets confirm the intuition of the proposed method leading to high classification accuracy.