Wittawat KositwattanarerkSoon Sheng OngFrédérique OggierMahidol UniversityNanyang Technological UniversityRaffles Institution2018-11-232018-11-232015-05-01IEEE Transactions on Information Theory. Vol.61, No.5 (2015), 2273-2282001894482-s2.0-84928542128https://repository.li.mahidol.ac.th/handle/20.500.14594/35813© 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>^-r)+ζ<inf>p</inf>^-r) of the cyclotomic field Q(ζ<inf>p</inf>^r), ≥ 1. Our construction has applications to coset encoding of algebraic lattice codes for block fading channels, and in particular for block fading wiretap channels.Mahidol UniversityComputer ScienceArticleSCOPUS10.1109/TIT.2015.2416340