Uniformly Packed Codes

Perfect and a particular kind of quasi-perfect binary block codes (in particular, nonlinear Preparata codes) are combined into a class of uniformly packed codes, on the basis of certain considerations about the packing of the code vectors. The authors consider the invariant properties of these codes, the necessary conditions for their existence, and the relationship between the codes and tactical configurations. They give combinatorial relationships between the sets of code vectors of different weight and the resulting formulas for determining the spectrum of weights and distances in the code. It is shown that in a uniformly packed code with zero vector the set of vectors of any one weight always forms a tactical configuration whose parameters are completely defined by the code parameters.