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We consider a class of symmetric Hopfield Networks, with nonpositive synapses and zero thresholds and address a variety of design and analysis issues conected with Unidirectional Error Correcting Coding applications of this class. We show that this class is naturally suited to work in a unidirectional error environment We give a necessary and sufficient condition for a set of vectors to be storable in a Nonpositive Network. We propose a simple word storage algorithm, which is amenable to on line implementation, and guarantees storage of all storage compatible words. We show that the storage algorithm creates a maximally fault tolerant network which is free from spurious stationary points, whenever that freedom is possible. We also give a word forgetting algorithm; a tight, deterministic bound on the storage capacity, and give conditions under which the network created by our storage scheme tolerates a given number of arbitrary physical faults.