Encoding for data recovery in storage systems

A computer program embodied on computer-readable storage and comprising code configured so as when run on one or more processing units to perform the method of reading from a storage medium in order to recover a group of information sectors, each information sector comprising a respective information payload;

• wherein the storage medium stores redundancy data comprising a plurality of separate redundancy codes for said group, each redundancy code being a linear sum of terms, each term in the sum being the information payload from a different respective one of the information sectors in said group weighted by a respective coefficient of a set of coefficients for the redundancy code, wherein said coefficients are selected according to a pseudorandom process;
• and
• wherein the method comprises, after the redundancy data has already been stored on the storage medium, performing a decoding process comprising:
• identifying a set of k′ information sectors from said group from which the respective information payloads are to be recovered based on the redundancy data;
• selecting k′ of the redundancy codes;
• determining a square matrix E in which each matrix column comprises the respective coefficients of a different one of the k′ information sectors, and each matrix row comprises the set of coefficients of a different one of the k′ redundancy codes, or vice versa;
• determining a matrix D being a matrix inverse of E;
• and
• recovering the k′ information payloads by computing:
• νi=Σj(di,j·rj), where νi is the information payload, i is an index denoting the respective information sector, and j is an index denoting each redundancy code r1, and where di,j are the matrix elements of the D, and Σj is the sum over the k′ redundancy codes, the computation being performed for i of each of the k′ information sectors.