the main connection as concerned to decoding and constructions are the A and B constructions of conway and sloane in SPLAG as mentioned by Malkevitch above. construction B is similar to A accept for an addition restriction, so for brevity i will only cover construction B.

(from SPLAG : conway & sloane)
Construction B:
let C be an (n,M,d) even binary code.

construction B: 1. x = (x_1,...x_n) is a lattice center iff x is congruent (mod 2) to a codeword of C  
                2. sum{x_i,n,i=0} = 0 (mod 4)  (this is the additional restriction from construction A)

the way in which the cluster centers are defined is through a coordinate array representations of points

coordinate array of a point x = (x_1,...x_n) with integer coordinates is obtained by writing the binary expansion of coordinates in x_i columnwise, beginning with the least significant digit.

ex
            * * * - these are in complement form
1's[ 0 1 0 1 0 1 0 1 ]
2's[ 0 1 1 0 0 1 1 0 ] = {4,3,2,1,0,-1,-2,-3}
4's[ 1 0 0 0 0 1 1 1 ]
8's[ 0 0 0 0 0 1 1 1 ]

construction B: a point x is a sphere center if the 1's row of the coordinate array is a codeword c in C and the 2's row has either even weight if the weight of c is divisible by 4 or odd weight if the weight is divisible by 2 but not 4.

the main connection as concerned to decoding and constructions are the A and B constructions of conway and sloane in SPLAG as mentioned by Malkevitch above. construction B is similar to A accept for an additional restriction, so for brevity i will only cover construction B.

(from SPLAG : conway & sloane)
Construction B:
let C be an (n,M,d) even binary code.

construction B: 1. x = (x_1,...x_n) is a lattice center iff x is congruent (mod 2) to a codeword of C  
                2. sum{x_i,n,i=0} = 0 (mod 4)  (this is the additional restriction from construction A)

the way in which the cluster centers are defined is through a coordinate array representations of points

coordinate array of a point x = (x_1,...x_n) with integer coordinates is obtained by writing the binary expansion of coordinates in x_i columnwise, beginning with the least significant digit.

ex
               * * * - these are in complement form
1's[ 0 1 0 1 0 1 0 1 ]
2's[ 0 1 1 0 0 1 1 0 ] = {4,3,2,1,0,-1,-2,-3}
4's[ 1 0 0 0 0 1 1 1 ]
8's[ 0 0 0 0 0 1 1 1 ]

construction B: a point x is a sphere center if the 1's row of the coordinate array is a codeword c in C and the 2's row has either even weight if the weight of c is divisible by 4 or odd weight if the weight is divisible by 2 but not 4.