English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A linear Fractional Network Coding (FNC) solution over $\mathbb{F}_q$ is alinear network coding solution over $\mathbb{F}_q$ in which the messagedimensions need not necessarily be the same and need not be the same as theedge vector dimension. Scalar linear network coding, vector linear networkcoding are special cases of linear FNC. In this paper, we establish theconnection between the existence of a linear FNC solution for a network over$\mathbb{F}_q$ and the representability over $\mathbb{F}_q$ of discretepolymatroids, which are the multi-set analogue of matroids. All previouslyknown results on the connection between the scalar and vector linearsolvability of networks and representations of matroids and discretepolymatroids follow as special cases. An algorithm is provided to constructnetworks which admit FNC solution over $\mathbb{F}_q,$ from discretepolymatroids representable over $\mathbb{F}_q.$ Example networks constructedfrom discrete polymatroids using the algorithm are provided, which do not admitany scalar and vector solution, and for which FNC solutions with the messagedimensions being different provide a larger throughput than FNC solutions withthe message dimensions being equal.

Linear Fractional Network Coding and Representable Discrete Polymatroids