Generalization of the lee weight to Zpk

Abstract

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