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Sum-networks: Dependency on Characteristic of the Finite Field under Linear Network Coding
Niladri Das, Brijesh Kumar Rai
Sum-networks are networks where all the terminals demand the sum of the symbols generated at the sources. It has been shown that for any finite set/co-finite set of prime numbers,…
On Fractional Linear Network Coding Solution of Multiple-Unicast Networks
Niladri Das, Brijesh Kumar Rai
It is known that there exists a multiple-unicast network which has a rate linear network coding solution if and only if the characteristic of the finite field belongs to a give…
Generalized Fano and non-Fano networks
Niladri Das, Brijesh Kumar Rai
It is known that the Fano network has a vector linear solution if and only if the characteristic of the finite field is ; and the non-Fano network has a vector linear solution i…
On Achievability of an Fractional Linear Network Code
Niladri Das, Brijesh Kumar Rai
It is known that there exists a network, called as the M-network, which is not scalar linearly solvable but has a vector linear solution for message dimension two. Recently, a gene…
On the Message Dimensions of Vector Linearly Solvable Networks
Niladri Das, Brijesh Kumar Rai
It is known that there exists a network which does not have a scalar linear solution over any finite field but has a vector linear solution when message dimension is [3]. It is…