Although non-linear over GF(2) the Preparata codes are linear over Z4 with the Lee distance.
We first describe the extended Preparata code of length
: the Preparata code is then derived by deleting one position.
The words of the extended code are regarded as pairs (X, Y) of 2m-tuples, each corresponding to subsets of the finite field GF(2m) in some fixed way.
The Preparata code is of length 2m+1 − 1, size 2k where k = 2m + 1 − 2m − 2, and minimum distance 5.