1. A method for dense encoding and retrieving of information represented in electronic computers, the method comprising (a) choosing an appropriate modulus m, positive integer n, corresponding to the number of bits to be encoding, and generating n×n matrix A with integer elements where the diagonal elements of A differs modulo m from all the other elements of their column, and where A can be written as matrix product BC where B is an n×t matrix, C is a t×n matrix, where t is less than n; (b) encoding the length-n vector x to the length-t vector xB, by vector-matrix product modulo m; (c) storing the length-t vector xB in physical computational devices; (d) retrieving the stored vector by computing xBC=xA by vector-matrix product modulo m; (e) for every coordinate of vector xBC=xA, filtering out the terms added as the linear combination of other coordinates of vector x.