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On the complexity of some coding problems (Corresp.)

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2 Author(s)

It is shown that the problem of finding a codeword with least weight and whose weight is not a multiple of k in a binary linear code belongs to the class of "nondeterministic polynomial (NP)-hard" problems for any k\geq 2 . Some other related problems are shown to belong to the same class. These results were motivated by a conjecture due to Berlekamp, McEliece, and van Tilborg that the problem of finding the Hamming distance of a code is NP-hard.

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Information Theory, IEEE Transactions on  (Volume:27 ,  Issue: 6 )