The decoding problem for BCH codes is often translated to the problem of finding a solution for a "key equation." There is a natural generalization of this key equation to one-point codes which also expresses the decoding problem. A solution to the key equation is a pair f, , where f is a function on the curve used to construct the code and is a differential, and both have poles only at the one-point Q. Kötter's generalization of the Berlekamp-Massey algorithm may be used to iteratively compute solutions to the key equation. The key ingredient in defining the algorithm is the existence of bases for K, the function field on the curve, and , the module of differentials, which are dual relative to the operator which takes the residue of a differential at Q.

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