Construction a of lattices over number fields and block fading (wiretap) coding
© 1963-2012 IEEE. We propose a lattice construction from totally real and complex multiplication fields, which naturally generalizes Construction A of lattices from p -ary codes obtained from the cyclotomic field Q(ζ<inf>p</inf>), p a prime, which in turn contains the so-called Construct...
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| Main Authors: | , , |
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| Format: | Article |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://repository.li.mahidol.ac.th/handle/123456789/35813 |
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| Institution: | Mahidol University |
| Summary: | © 1963-2012 IEEE. We propose a lattice construction from totally real and complex multiplication fields, which naturally generalizes Construction A of lattices from p -ary codes obtained from the cyclotomic field Q(ζ<inf>p</inf>), p a prime, which in turn contains the so-called Construction A of lattices from binary codes as a particular case. We focus on the maximal totally real subfield Q(ζ<inf>p</inf><sup>-r</sup>)+ζ<inf>p</inf><sup>-r</sup>) of the cyclotomic field Q(ζ<inf>p</inf><sup>r</sup>), ≥ 1. Our construction has applications to coset encoding of algebraic lattice codes for block fading channels, and in particular for block fading wiretap channels. |
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