1. A process for protecting against loss and for enhancing accessibility in storage or memory, or protecting against loss and enhancing speed of transmission on communication paths, of information which is represented in storage or memory, or represented as data signals on communication paths, said information comprising data elements, each said data element representable as an element of a finite field or computational structure, said process comprising transforming and breaking apart said information among a set of smaller assemblages of elements of said finite field or computational structure, and dispersing said information by transmitting said smaller assemblages in the form of said data signals carried on multiple communication paths, or by transmitting said smaller assemblages at different times in the form of said data signals carried on a single communication path, or by storing said assemblages in multiple storage or memory locations, in a manner that is expected to yield no fewer than a required number of said assemblages, said step of transforming and breaking apart comprising representing said information by N elements of said field or computational structure, grouping said N elements into N/m groups, each containing m elements, where N is greater than m, and hence there are more than one of said groups, selecting a set of vectors {a.sub.i :i=1,. .. , n}, each of said vectors having m elements of said field or computational structure, there being an arbitrarily high probability that any subset of m of the vectors are linearly independent, generating a set of elements {C.sub.i,r : i=1,. .. , n, r=1,. .. , N/m} for assembly into n said assemblages, each element c.sub.i,r being generated as the product of a vector a.sub.i times the elements of the r-th said group of elements, and assembling the n assemblages such that the i-th assemblage comprises the elements {C.sub.i,r : r=1,. .. , N/m}.