Generalized Fano and nonFano networks
Abstract
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 nonFano 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 nonFano networks it has been shown that linear network coding is insufficient. In this paper we generalize the properties of Fano and nonFano networks. Specifically, by adding more nodes and edges to the Fano network, we construct 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 $\{p_1,p_2,\ldots,p_l\}$. Similarly, by adding more nodes and edges to the nonFano network, we construct a network which has a vector linear solution for any vector dimension if and only if the characteristic of the finite field does not belong to an arbitrary given set of primes $\{p_1,p_2,\ldots,p_l\}$.
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 arXiv:
 arXiv:1609.05815
 Bibcode:
 2016arXiv160905815D
 Keywords:

 Computer Science  Information Theory