Induced weights on quotient modules and an application to error correction in coherent networks

Abstract

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 error-correction in the presence of adversarial errors. We outline this connection, extending the linear network coding scheme introduced by Yang et al.