## Abstract

There is a rich theory of relations between lattices and linear codes over finite fields. However, this theory has been developed mostly with lattice codes for the Gaussian channel in mind. In particular, different versions of what is called Construction A have connected the Hamming distance of the linear code to the Euclidean structure of the lattice.

This paper concentrates on developing a similar theory, but for fading channel coding instead. First, two versions of Construction A from number fields are given. These are then extended to division algebra lattices. Instead of the Euclidean distance, the Hamming distance of the finite codes is connected to the product distance of the resulting lattices, that is the minimum product distance and the minimum determinant respectively.

Original language | English |
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Title of host publication | IEEE International Symposium on Information Theory - Proceedings |

Publisher | IEEE |

Pages | 2326-2330 |

Number of pages | 5 |

ISBN (Electronic) | 978-147995186-4 |

DOIs | |

Publication status | Published - 2014 |

MoE publication type | A4 Article in a conference publication |

Event | IEEE International Symposium on Information Theory - Honolulu, United States Duration: 29 Jun 2014 → 4 Jul 2014 |

### Publication series

Name | IEEE International Symposium on Information Theory |
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Publisher | IEEE |

ISSN (Electronic) | 2157-8095 |

### Conference

Conference | IEEE International Symposium on Information Theory |
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Abbreviated title | ISIT |

Country | United States |

City | Honolulu |

Period | 29/06/2014 → 04/07/2014 |