Correspondence identifies certain coding problems as NP-complete, suggesting polynomial-time solutions may not exist.
MEMBER, IEEE, AND HENK C. A. V~ TILBORG The fact that the general decoding problem for linear codes and the general problem of finding the weights of a linear code are both NP-complete is shown. This strongly suggests, but does not rigorously imply, that no algorithm for either of these problems which runs in polynomial time exists.
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Berlekamp et al. (1978) studied this question.
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