Dense memory with high order neural networks

The author presents a specific high-order neural network design that can store using n neutrons, any number M, 1⩽ M⩽2ⁿ, of any of the binomial n-strings; in a schematic representation the model requires only 5n+M (1+2n) edges. With sufficiently high gains, the only stable attractors are the memories. Thus the memory model amounts to a solution of a version of the fundamental memory problem. The memory model can be used in error-correcting decoding of any binary string code and, in particular, has been used to correct single errors in a linear code with n=7 and single and double errors in a nonlinear code with n=11