In a network with capacity h for multicast, information Xh=(X1, X2, , Xh) can be transmitted from a source node to sink nodes without error by a linear network code. Furthermore, secret information Sr=(S1, S2, , Sr) can be transmitted securely against wiretappers by k-secure network coding for k h-r. In this case, no information of the secret leaks out even if an adversary wiretaps k edges, i.e. channels. However, if an adversary wiretaps k+1 edges, some Si may leak out explicitly. In this paper, we propose strongly k-secure network coding based on strongly secure ramp secret sharing schemes. In this coding, no information leaks out for every (Si1, Si2, ,Sir-j) even if an adversary wiretaps k+j channels. We also give an algorithm to construct a strongly k-secure network code directly and a transform to convert a nonsecure network code to a strongly k-secure network code. Furthermore, some sufficient conditions of alphabet size to realize the strongly k-secure network coding are derived for the case of k < h-r.

We propose two kinds of architectures for implementing large-scale opto-electronic neural networks. These architectures are based on time- and frequency-division multiplexing (TDM and FDM) techniques, respectively, in which both the neuron state vector and the interconnection matrix are divided in the time- and frequency-domains. The computer simulations, which were carried out for the Hopfield associative memories in the neuron number of 400 and the memory number of 20, have shown their usefulness, providing almost the same recognition rate as the conventional architectures. Using the TDM technique, moreover, we experimentally demonstrated an opto-electronic implementation of the Hopfield associative memory. The experimental results showed that the number of the neurons was effectively increased. We further discuss how to construct the FDM system experimentally.