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1978•IEEE Transactions on Information TheoryOpen access

On the inherent intractability of certain coding problems (Corresp.)

Elwyn R. Berlekamp, Robert J. McEliece, H. van Tilborg

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Abstract

The fact that the general decoding problem for linear codes and the general problem of finding the weights of a linear code are both NP-complete is shown. This strongly suggests, but does not rigorously imply, that no algorithm for either of these problems which runs in polynomial time exists.

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What this paper is about

The fact that the general decoding problem for linear codes and the general problem of finding the weights of a linear code are both NP-complete is shown. This strongly suggests, but does not rigorously imply, that no algorithm for either of these problems which runs in polynomial time exists.

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Available abstract

The fact that the general decoding problem for linear codes and the general problem of finding the weights of a linear code are both NP-complete is shown. This strongly suggests, but does not rigorously imply, that no algorithm for either of these problems which runs in polynomial time exists.

Key concepts: Decoding methods, Coding (social sciences), Algorithm, List decoding, Mathematics, Computer science, Linear code, Discrete mathematics

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