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APPROX

2009

Springer

2009

Springer

The Nearest Codeword Problem (NCP) is a basic algorithmic question in the theory of error-correcting codes. Given a point v ∈ Fn 2 and a linear space L ⊆ Fn 2 of dimension k NCP asks to ﬁnd a point l ∈ L that minimizes the (Hamming) distance from v. It is well-known that the nearest codeword problem is NP-hard. Therefore approximation algorithms are of interest. The best eﬃcient approximation algorithms for the NCP to date are due to Berman and Karpinski. They are a deterministic algorithm that achieves an approximation ratio of O(k/c) for an arbitrary constant c, and a randomized algorithm that achieves an approximation ratio of O(k/ log n). In this paper we present new deterministic algorithms for approximating the NCP that improve substantially upon the earlier work. Speciﬁcally, we obtain: – A polynomial time O(n/ log n)-approximation algorithm; – An nO(s) time O(k log(s) n/ log n)-approximation algorithm, where log(s) n stands for s iterations of log, e.g., log(2) ...

Related Content

Added |
25 May 2010 |

Updated |
25 May 2010 |

Type |
Conference |

Year |
2009 |

Where |
APPROX |

Authors |
Noga Alon, Rina Panigrahy, Sergey Yekhanin |

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