Lattices which are good for (almost) everything

@article{Erez2005LatticesWA,
  title={Lattices which are good for (almost) everything},
  author={Uri Erez and Simon Litsyn and Ram Zamir},
  journal={IEEE Transactions on Information Theory},
  year={2005},
  volume={51},
  pages={3401-3416}
}
We define an ensemble of lattices, and show that for asymptotically high dimension most of its members are simultaneously good as sphere packings, sphere coverings, additive white Gaussian noise (AWGN) channel codes and mean-squared error (MSE) quantization codes. These lattices are generated by applying Construction A to a random linear code over a prime field of growing size, i.e., by "lifting" the code to /spl Ropf//sup n/. 
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