2016/09/19 by Niladri Das, Das, Niladri, Brijesh Kumar Rai +1
Computer Science · Mathematics · #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1609.05815
arxiv created 2016/09/19 · arxiv updated 2016/09/20
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 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 \p1,p2,…,pl\. Similarly, by adding more nodes and edges to the non-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 does not belong to an arbitrary given set of primes \p1,p2,…,pl\.