On the complexity of some coding problems (Corresp.)

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.