Generalization of the lee weight to ?p?

Abstract

We introduce a new extension of the Lee weight to ?p? and later to Galois rings GR(p?,m). The weight we define is a non-homogeneous weight and is different than the one that is generally labeled as "generalized Lee weight". Unlike the case of generalized Lee weight, we define a distance-preserving Gray map from (?p?, extended Lee distance)to (Fpp??¹, Hamming distance), thus making our extension practical for coding theory purposes.