A Metric for Codes over Residue Class Rings

The Lee weight function Ли $w:\mathbb Z_4\mapsto\mathbb N_0$, $0\mapsto 0$, 1, $3\mapsto 1$, $2\mapsto 2$, used by Calderbank et al. ( IEEE Trans. Inf. Theory, IT-40, No. 2, 301–319 (1994)) for the representation of some nonlinear binary codes as linear codes over $\mathbb Z_4$ is generalized to the residue class ring $\mathbb Z_m$ of integers with an arbitrary modulus $m$. This generalized weight is a unique function having certain homogeneity properties, which are desirable for coding-theoretic purposes.