Generalization of the lee weight to Ζpᵏ

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 "generalized 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.