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

We consider distance functions on a quotient module M/K induced by distance functions on a module M. We define error-correction for codes in M/K with respect to induced distance functions. For the case that the metric is induced by a homogeneous weight, we derive analogues of the Plotkin and Elias-Bassalygo bounds and give their asymptotic versions. These results have applications to coherent network errorcorrection in the presence of adversarial errors. We outline this connection, extending the linear network coding scheme introduced by Yang et al.