Publication: Constructions a of lattices from number fields and division algebras
Issued Date
2014-01-01
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ISSN
21578095
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2-s2.0-84906536017
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Mahidol University
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SCOPUS
Bibliographic Citation
IEEE International Symposium on Information Theory - Proceedings. (2014), 2326-2330
Suggested Citation
Roope Vehkalahti, Wittawat Kositwattanarerk, Frédérique Oggier Constructions a of lattices from number fields and division algebras. IEEE International Symposium on Information Theory - Proceedings. (2014), 2326-2330. doi:10.1109/ISIT.2014.6875249 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/33756
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Title
Constructions a of lattices from number fields and division algebras
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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. © 2014 IEEE.