Method and apparatus for performing arithmetic operations on Galois fields and their extensions

摘要

The invention relates to an arithmetic unit (AU) in combination with an algebraic block ECC decoder for controlling errors in an electronically recorded digital data message by performing at least one of a plurality of predetermined arithmetic operations on the data message in one or more of a plurality of subfields of a first GF(212) or a second GF(28) finite field. The arithmetic operations are selected either from a first group of operations associated with a first subfield GF(24) as cubically extended to the first finite field GF(212) or as quadratically extended to the second finite field GF(28), or selected from a second group of operations associated with a second subfield GF(26) as quadratically extended to the first finite field GF(212).