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We consider distance functions on a quotient module $M/K$ induced by distancefunctions on a module $M$. We define error-correction for codes in $M/K$ withrespect to induced distance functions. For the case that the metric is inducedby a homogeneous weight, we derive analogues of the Plotkin and Elias-Bassalygobounds and give their asymptotic versions. These results have applications tocoherent network error-correction in the presence of adversarial errors. Weoutline this connection, extending the linear network coding scheme introducedby Yang et al.

Induced Weights on Quotient Modules and an Application to Error Correction in Coherent Networks