A Class of Non-Linearly Solvable Networks

Abstract

For each integer $m\ge 2$, a network is constructed which is solvable over an alphabet of size $m$ but is not solvable over any smaller alphabets. If $m$ is composite, then the network has no vector linear solution over any $R$-module alphabet and is not asymptotically linear solvable over any finite-field alphabet. The network's capacity is shown to equal one, and when $m$ is composite, its linear capacity is shown to be bounded away from one for all finite-field alphabets.

Submitted to IEEE Transactions on Information Theory January 14th 2016

References in corpus (2)

• On Vector Linear Solvability of Multicast Networks
• Multicast Network Coding and Field Sizes

Cited by in corpus (4)

• Circular-shift Linear Network Coding
• Circular-shift Linear Network Codes with Arbitrary Odd Block Lengths
• Linear Network Coding over Rings, Part I: Scalar Codes and Commutative Alphabets
• A Local Perspective on the Edge Removal Problem