GENERALIZATION OF THE LEE WEIGHT TO Ζpk

GENERALIZATION OF THE LEE WEIGHT TO Ζ_p^k

Bahattin Yildiz    Zeynep Odemis Ozger    

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Abstract

We introduce a new extension of the Lee weight to Ζ_p^k and later to Galois rings GR(p^k,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 (Ζ_p^k, extended Lee distance)to (F_p^pk-1, Hamming distance), thus making our extension practical for coding theory purposes.

Keywords

Lee weight, extended, Gray map.