| CPC H03M 13/6516 (2013.01) | 15 Claims |
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1. A method for decoding an error correction code by a decoding device comprising a processor, comprising:
acquiring, by the processor, a Galois field equation corresponding to the error correction code, wherein a total length of the error correction code is a predetermined number of digits;
determining, by the processor, a target relational expression corresponding to a plurality of error locations after decoding the error correction code based on the Galois field equation, wherein the target relational expression is derived based on Vieta's formulas;
determining, by the processor, a plurality of conjugate location pairs based on the target relational expression;
for each of the plurality of conjugate location pairs, determining, by the processor, a first polynomial corresponding to an exponential coefficient of a first location in the conjugate location pair and a second polynomial corresponding to an exponential coefficient of a second location in the conjugate location pair, based on a correspondence table between exponents and polynomials in a Galois field;
performing, by the processor, an exclusive OR operation on coefficients of the first polynomial and the second polynomial to obtain an exclusive OR result;
determining, by the processor, the first location and the second location as error locations, in a case that the exclusive OR result matches a target coefficient of the Galois field equation; and
decoding, by the processor, the error correction code based on the error locations.
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