Title :
The intractability of computing the minimum distance of a code
Author :
Vardy, Alexander
Author_Institution :
Coordinated Sci. Lab., Illinois Univ., Urbana, IL, USA
fDate :
11/1/1997 12:00:00 AM
Abstract :
It is shown that the problem of computing the minimum distance of a binary linear code is NP-hard, and the corresponding decision problem is NP-complete. This result constitutes a proof of the conjecture of Berlekamp, McEliece, and van Tilborg (1978). Extensions and applications of this result to other problems in coding theory are discussed
Keywords :
computational complexity; decision theory; linear codes; Berlekamp McEliece and van Tilborg conjecture; NP-complete problem; NP-hard problem; binary linear code; coding theory; decision problem; minimum distance; Combinatorial mathematics; Distributed computing; History; Linear code; Maximum likelihood decoding; NP-complete problem; Parity check codes; Polynomials; Turing machines; Vectors;
Journal_Title :
Information Theory, IEEE Transactions on
