GENERALIZATION OF THE LEE WEIGHT TO Ζpk

Year 2012, Volume: 2 Issue: 2, 145 - 153, 01.12.2012

B. Yıldız Z. Ödemiş Özger

Abstract

We introduce a new extension of the Lee weight to Zpk 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 Zpk , extended Lee distance to F p k−1 p , Hamming distance , thus making our extension practical for coding theory purposes.

Keywords

Lee weight, extended, Gray map

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