Abstract: The present invention provides a generalized method for standard Galois Field operational schemes used in Advanced RAID parity calculations. This method places the standard-field and ring operations in their generalized context of linear operations, which can be described by matrices over the Galois Field with two elements (GF(2)). To ensure recovery of information, certain conditions on these matrices are imposed. A plurality of methods for generating such matrices are provided, thereby increasing the range of computational techniques for parity calculation. Further, the method provides increased flexibility and scope in finding a more efficient computational scheme that is adapted to a particular hardware or software implementation.