Decoding
There are many algorithms for decoding BCH codes. The most common ones follow this general outline:
- Calculate the syndromes sj for the received vector
- Determine the number of errors t and the error locator polynomial Λ(x) from the syndromes
- Calculate the roots of the error location polynomial to find the error locations Xi
- Calculate the error values Yi at those error locations
- Correct the errors
During some of these steps, the decoding algorithm may determine that the received vector has too many errors and cannot be corrected. For example, if an appropriate value of t is not found, then the correction would fail. In a truncated (not primitive) code, an error location may be out of range. If the received vector has more errors than the code can correct, the decoder may unknowingly produce an apparently valid message that is not the one that was sent.
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