| CPC H03M 13/6516 (2013.01) | 10 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 first traversal range based on the target relational expression and the predetermined number of digits;
determining, by the processor, a first error location from values comprised in the first traversal range;
determining, by the processor, a second error location based on the target relational expression and the first error location; and
decoding, by the processor, the error correction code based on the first error location and the second error location.
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