1. A system that transforms data involving a secure format from which the data is configured to be recovered, the system comprising: at least one processor that produces a first quantity (W) of data inputs from input data; one or more transforming components that perform a transformation process on the W data inputs to transform the input data into the secure format using Galois field operations and a generator matrix having a generator matrix structure characterized as being invertible in all subsets encounterable during recovery operations of the input data based on a recovery matrix; a generating component that generates a second quantity (H) of discrete output data streams from the W data inputs; wherein H is greater than, or greater than or equal to, W and the transformation process includes: for each of the W inputs, producing an H-sized intermediary; and processing a plurality of H-sized intermediaries into the H discrete output data streams; wherein the W data inputs are configured to be recovered via a recovery process involving recovery coefficients of the recovery matrix, the recovery process producing the W data inputs from any W members of the H discrete output data streams; and wherein the system is configured to recover the data via the recovery process, wherein the recovery process utilizes the recovery coefficients of the recovery matrix to recover the input data back from the secure format, the recovery coefficients organizable into a recovery matrix structure characterized as being invertible with regard to the coefficients of the transformation matrix in all subsets of the matrix structure encounterable during recovery of the input data.