### Abstract

In this paper, an exact distance spectrum formula for the largest minimum Hamming distance of finite-length binary block codes is presented. The exact formula indicates that the largest minimum distance of finite-length block codes can be fully characterized by the information spectrum of the Hamming distance between two independent and identically distributed (i.i.d.) random codewords. The distance property of finite-length block codes is then connected to the distance spectrum. A side result of this work is a new lower bound to the largest minimum distance of finite-length block codes. Numerical examinations show that the new lower bound improves the finite-length Gilbert-Varshamov lower bound and can reach the minimum distance of existing finite-length block codes.

Original language | English |
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Title of host publication | 2017 IEEE Information Theory Workshop, ITW 2017 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 419-423 |

Number of pages | 5 |

ISBN (Electronic) | 9781509030972 |

DOIs | |

State | Published - 31 Jan 2018 |

Event | 2017 IEEE Information Theory Workshop, ITW 2017 - Kaohsiung, Taiwan Duration: 6 Nov 2017 → 10 Nov 2017 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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Volume | 2018-January |

ISSN (Print) | 2157-8095 |

### Conference

Conference | 2017 IEEE Information Theory Workshop, ITW 2017 |
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Country | Taiwan |

City | Kaohsiung |

Period | 6/11/17 → 10/11/17 |

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## Cite this

*2017 IEEE Information Theory Workshop, ITW 2017*(pp. 419-423). (IEEE International Symposium on Information Theory - Proceedings; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ITW.2017.8277923