Digital data e.g. digital image, decoding method for e.g. microcomputer, involves calculating polynomials by applying decoding algorithm for specified input, and determining list of polynomials which factorize completely on Galois group

摘要

The method involves calculating a set of polynomials by applying an iterative decoding algorithm from a syndrome for a specified input, and determining a list of polynomials, from the set of polynomials, which factorize completely on a Galois group. A missing component of the syndrome is calculated from the polynomials of the list to obtain an extended syndrome, and a decoding estimate of an emitted word is determined for an ordered pair. One of the determined decoding estimates is chosen, where the chosen estimate is found at the smallest hamming distance of a received word. Independent claims are also included for the following: (1) a method for decoding an algebraic geometric code by an aggregation (2) a device for decoding digital data (3) a device for decoding an algebraic geometric code by an aggregation (4) an information storing unit having computer programming instructions for implementing a digital data decoding method (5) a computer programming product stored in a programmable apparatus for implementing a digital data decoding method (6) a removable information storing unit having computer programming instructions for implementing a digital data decoding method.