Is code equivalence easy to decide?

@article{Petrank1997IsCE,
  title={Is code equivalence easy to decide?},
  author={Erez Petrank and Ron M. Roth},
  journal={IEEE Trans. Information Theory},
  year={1997},
  volume={43},
  pages={1602-1604}
}
We study the computational difficulty of deciding whether two matrices generate equivalent linear codes, i.e., codes that consist of the same codewords up to a fixed permutation on the codeword coordinates. We call this problem Code Equivalence. Using techniques from the area of interactive proofs, we show on the one hand, that under the assumption that the polynomial-time hierarchy does not collapse, Code Equivalence is not NP-complete. On the other hand, we present a polynomial-time reduction… CONTINUE READING
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