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arXiv · 1404.2904

Construction A of Lattices over Number Fields and Block Fading Wiretap Coding

Wittawat Kositwattanarerk·Soon Sheng Ong·Frédérique Oggier
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Abstract

We propose a lattice construction from totally real and CM fields, which naturally generalizes the Construction A of lattices from $p$-ary codes obtained from the cyclotomic field $\mathbb{Q}(ζ_p)$, $p$ 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 $\mathbb{Q}(ζ_{p^r}+ζ_{p}^{-r})$ of the cyclotomic field $\mathbb{Q}(ζ_{p^r})$, $r\geq 1$. Our construction has applications to coset encoding of algebraic lattice codes, and we detail the case of coset encoding of block fading wiretap codes.

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Wittawat Kositwattanarerk, Soon Sheng Ong, Frédérique Oggier. 2014-12-12. Construction A of Lattices over Number Fields and Block Fading Wiretap Coding. https://doi.org/10.1109/tit.2015.2416340

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