COMPUTING THE WEIGHT DISTRIBUTION OF A SET OF POINTS OBTAINED BY SCALING, SHIFTING, AND TRUNCATING A LATTICE

A method is developed to compute the weight distribution of a set of p oints obtained from a lattice. The lattice is scaled (with possibly no nequal factors) along different dimensions, is shifted to an arbitrary point, and its lower dimensional subspaces are truncated within given shaping regions. Each branch in the lattice trellis diagram is labele d by the weight distribution of the corresponding coset incorporating the effects of scaling, shifting, and truncation. The weight distribut ion is obtained by multiplying the weight distribution of the serial b ranches and then adding the result over parallel paths.