Lattices based on linear codes
The Conway and Sloane construction A method is applied to evaluation of a class of lattices. The points of the lattices belong to a scaled set of n-dimensional vectors with integer components and the lattices constructed with the aide of linear over GF(p) codes, p is prime. It is known that the Minkowski-Hlawka bound on the normalized logarithm of packing density is attained asymptotically by such construction of lattices. We show that the capacity of an AWGN channel without restriction can be also attained by these class of lattices.
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