The automatic eveolution of neural networks is both an attractive and a rewarding task. The connectivity matrix is the most common way of directly encoding a neural network for the purpose of genetic optimization. However, this representation presents several disadvantages mostly stemming from its inherent redundancy and its lack of rebustness. We propose a novel representation scheme for encoding complete strictly-layered feedforward neural networks and prove that it is optimal in the sense that it utilizes the minimum possible number of bits. We argue that this scheme has a number of important advantages over the direct encoding of the connectivity matrix. It does not suffer from the curse of dimensionality, it allows only legal networks to be represented which relieves the genetic algorithm from a number of checking and rejections, and the mapping from the genotypes to phenotypes is one-to-one. Additionally, the resulting networks have a simpler structure assuring an easier learning phase.