On covering problems of codes

@article{Francs2007OnCP,
  title={On covering problems of codes},
  author={Mar{\'i}a del Mar Franc{\'e}s and Ami Litman},
  journal={Theory of Computing Systems},
  year={2007},
  volume={30},
  pages={113-119}
}
LetC be a binary code of lengthn (i.e., a subset of {0, 1} n ). TheCovering Radius of C is the smallest integerr such that each vector in {0, 1} n is at a distance at mostr from some code word. Our main result is that the decision problem associated with the Covering Radius of arbitrary binary codes is NP-complete. This result is established as follows. TheRadius of a binary codeC is the smallest integerr such thatC is contained in a radius-r ball of the Hamming metric space 〈{0, 1} n ,d〉. It… CONTINUE READING

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