### Abstract

We study the performance of the Metropolis algorithm for the problem of finding a code word of weight less than or equal to M, given a generator matrix of an [n; κ]-binary linear code. The algorithm uses the set Sκ of all κ × κ invertible matrices as its search space where two elements are considered adjacent if one can be obtained from the other via an elementary row operation (i.e by adding one row to another or by swapping two rows.) We prove that the Markov chains associated with the Metropolis algorithm mix rapidly for suitable choices of the temperature parameter T. We ran the Metropolis algorithm for a number of codes and found that the algorithm performed very well in comparison to previously known experimental results.

Original language | English |
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Title of host publication | GECCO 2014 - Proceedings of the 2014 Genetic and Evolutionary Computation Conference |

Publisher | Association for Computing Machinery (ACM) |

Pages | 485-492 |

Number of pages | 8 |

ISBN (Print) | 9781450326629 |

DOIs | |

Publication status | Published - 2014 |

Event | 16th Genetic and Evolutionary Computation Conference, GECCO 2014 - Vancouver, BC, Canada Duration: 12-07-2014 → 16-07-2014 |

### Conference

Conference | 16th Genetic and Evolutionary Computation Conference, GECCO 2014 |
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Country | Canada |

City | Vancouver, BC |

Period | 12-07-14 → 16-07-14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*GECCO 2014 - Proceedings of the 2014 Genetic and Evolutionary Computation Conference*(pp. 485-492). Association for Computing Machinery (ACM). https://doi.org/10.1145/2576768.2598274

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*GECCO 2014 - Proceedings of the 2014 Genetic and Evolutionary Computation Conference.*Association for Computing Machinery (ACM), pp. 485-492, 16th Genetic and Evolutionary Computation Conference, GECCO 2014, Vancouver, BC, Canada, 12-07-14. https://doi.org/10.1145/2576768.2598274

**Performance of metropolis algorithm for the minimum weight code word problem.** / Ajitha Shenoy, K. B.; Biswas, Somenath; Kurur, Piyush P.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Performance of metropolis algorithm for the minimum weight code word problem

AU - Ajitha Shenoy, K. B.

AU - Biswas, Somenath

AU - Kurur, Piyush P.

PY - 2014

Y1 - 2014

N2 - We study the performance of the Metropolis algorithm for the problem of finding a code word of weight less than or equal to M, given a generator matrix of an [n; κ]-binary linear code. The algorithm uses the set Sκ of all κ × κ invertible matrices as its search space where two elements are considered adjacent if one can be obtained from the other via an elementary row operation (i.e by adding one row to another or by swapping two rows.) We prove that the Markov chains associated with the Metropolis algorithm mix rapidly for suitable choices of the temperature parameter T. We ran the Metropolis algorithm for a number of codes and found that the algorithm performed very well in comparison to previously known experimental results.

AB - We study the performance of the Metropolis algorithm for the problem of finding a code word of weight less than or equal to M, given a generator matrix of an [n; κ]-binary linear code. The algorithm uses the set Sκ of all κ × κ invertible matrices as its search space where two elements are considered adjacent if one can be obtained from the other via an elementary row operation (i.e by adding one row to another or by swapping two rows.) We prove that the Markov chains associated with the Metropolis algorithm mix rapidly for suitable choices of the temperature parameter T. We ran the Metropolis algorithm for a number of codes and found that the algorithm performed very well in comparison to previously known experimental results.

UR - http://www.scopus.com/inward/record.url?scp=84905715102&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84905715102&partnerID=8YFLogxK

U2 - 10.1145/2576768.2598274

DO - 10.1145/2576768.2598274

M3 - Conference contribution

SN - 9781450326629

SP - 485

EP - 492

BT - GECCO 2014 - Proceedings of the 2014 Genetic and Evolutionary Computation Conference

PB - Association for Computing Machinery (ACM)

ER -