### Abstract

Iterative techniques have been proposed for decoding linear binary block codes over erasure channels. The performance of such decoding techniques depends on the parity-check matrices used, and in partivular, on the numbers and sizes of stopping sets of these matrices. In the 2004 Shannon lecture, McElliece presented an expression for the number of stopping sets of size three for a full-rank parity-check matrix of the Hamming code. In this paper, we present an expression for the number of stopping sets of any given size for the same parity-check matrix.

Original language | Undefined/Unknown |
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Title of host publication | Proceedings of the twenty-seventh symposium on information theory in the Benelux |

Editors | RL Lagendijk, JH Weber |

Place of Publication | Enschede |

Publisher | WIC |

Pages | 61-68 |

Number of pages | 8 |

ISBN (Print) | 9071048225 |

Publication status | Published - 2006 |

Event | Twenty-seventh symposium on information theory in the Benelux, Noordwijk, The Netherlands - Delft, noordwijk Duration: 8 Jun 2006 → 9 Jun 2006 |

### Publication series

Name | |
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Publisher | WIC |

### Conference

Conference | Twenty-seventh symposium on information theory in the Benelux, Noordwijk, The Netherlands |
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City | noordwijk |

Period | 8/06/06 → 9/06/06 |

### Keywords

- conference contrib. refereed
- Conf.proc. > 3 pag

## Cite this

Abdel-Ghaffar, KAS., & Weber, JH. (2006). Enumeration of stopping sets of full-rank parity-check matrices of hammng codes. In RL. Lagendijk, & JH. Weber (Eds.),

*Proceedings of the twenty-seventh symposium on information theory in the Benelux*(pp. 61-68). WIC.