Abstract: Described are methods, systems, and apparatus, including computer program products for error correction coding and decoding procedures for data storage or transfer. A plurality of data blocks is received. A plurality of checksum blocks are generated by multiplying the plurality of data blocks by a coding matrix, where the coding matrix comprises values of at least one basic interpolation polynomial and the multiplying is according to a finite field arithmetic for a finite field comprising all possible values of the plurality of data blocks and the plurality of coding blocks. The plurality of data blocks and the plurality of checksum blocks are stored in a data storage medium.

Abstract: Described are methods, systems, and apparatus, including computer program products for error correction coding and decoding procedures for data storage or transfer. A plurality of data blocks is received. A plurality of checksum blocks are generated by multiplying the plurality of data blocks by a coding matrix, where the coding matrix comprises values of at least one basic interpolation polynomial and the multiplying is according to a finite field arithmetic for a finite field comprising all possible values of the plurality of data blocks and the plurality of coding blocks. The plurality of data blocks and the plurality of checksum blocks are stored in a data storage medium.

Abstract: A method and system for recovering data written onto a storage device when system failure and/or damage occur during use is provided. A memory of the storage device is divided into a plurality of information zones, for storing data as a codeword set, and a plurality of check zones, for storing checksums, of equal size selected from different parts of the storage device. A computing unit calculates etalon checksums with an established formula during each write data operation for each codeword set in the information zones. If failure, damage or data corruption occurs, computing unit calculates current checksums using an established formula. The values of the stored etalon checksums and the current checksums are used for data recovery, which is performed by solving the system of equations, received from the formula for computing the checksums. Parallel calculation schemes are used in checksum computing and for data recovery.