Abstract: A method of calculating single and dual parity for a networked array of storage elements is presented. The method includes deriving a first set of n relationships where each of the first set of n relationships consists of an XOR statement equaling zero. Each of the first set of n relationships contains n data symbols from n storage elements and one parity symbol from a first set of parity symbols. The method also includes deriving a second set of n+1 relationships where each of the second set of n+1 relationships consists of an XOR statement equaling zero, containing at least n?1 data symbols from at least n?1 storage elements and one parity symbol from a second set of parity symbols. Using both the first and second sets of derived relationships, scripts are generated to resolve unresolved symbols resulting from possible single- and dual-storage element failure combinations.

Abstract: A disk array utilizes a surviving relationship algorithm for generating parity terms. During a drive failure, a script corresponding to the failure mode (e.g., single storage element failure or dual storage element failure) is executed. The script reconstructs data by deriving a surviving relationship matrix from a seed matrix, sending the resulting surviving relationship matrix to parity/data generators in the storage controller, and generating P parity and Q parity symbols based on the inputs from the relationship matrix. The surviving relationship matrix is independent of symbol position (i.e., row, column, or diagonal) and further ensures that all data is reconstructable after single or dual storage element failures.