# Generalized Fano and non-Fano networks

@article{Das2016GeneralizedFA, title={Generalized Fano and non-Fano networks}, author={Niladri Das and Brijesh Kumar Rai}, journal={2017 Twenty-third National Conference on Communications (NCC)}, year={2016}, pages={1-6} }

It is known that the Fano network has a vector linear solution if and only if the characteristic of the finite field is 2; and the non-Fano network has a vector linear solution if and only if the characteristic of the finite field is not 2. Using these properties of Fano and non-Fano networks it has been shown that linear network coding is insufficient. In this paper we generalize the properties of Fano and non-Fano networks. Specifically, by adding more nodes and edges to the Fano network, we…

## 2 Citations

### On fractional linear network coding solution of multiple-unicast networks

- Mathematics, Computer Science2017 Twenty-third National Conference on Communications (NCC)
- 2017

It is shown that for any non-zero positive rational number k/n, there exists a multiple-unicast network which has a rate k/N fractional linear network coding solution if and only if the characteristic of the finite field belongs to a given finite or co-finite set of primes.

### Generalized Fano and non-Fano networks

- Computer Science, Mathematics2017 Twenty-third National Conference on Communications (NCC)
- 2017

This paper generalizes the properties of Fano and non-Fano networks and constructs a network which has a vector linear solution for any vector dimension if and only if the characteristic of the finite field belongs to an arbitrary given set of primes.

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This paper generalizes the properties of Fano and non-Fano networks and constructs a network which has a vector linear solution for any vector dimension if and only if the characteristic of the finite field belongs to an arbitrary given set of primes.