As state of the art neural networks (NNs) continue to grow in size, their resource-efficient implementation becomes ever more important. In this paper, we introduce a compression scheme that reduces the number of computations required for NN inference on reconfigurable hardware such as FPGAs. This is achieved by combining pruning via regularized training, weight sharing and linear computation coding (LCC). Contrary to common NN compression techniques, where the objective is to reduce the memory used for storing the weights of the NNs, our approach is optimized to reduce the number of additions required for inference in a hardware-friendly manner. The proposed scheme achieves competitive performance for simple multilayer perceptrons, as well as for large scale deep NNs such as ResNet-34.