An algebraic approach to network coding
IEEE/ACM Transactions on Networking (TON)
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Polynomial time algorithms for multicast network code construction
IEEE Transactions on Information Theory
Insufficiency of linear coding in network information flow
IEEE Transactions on Information Theory
Nonreversibility and Equivalent Constructions of Multiple-Unicast Networks
IEEE Transactions on Information Theory
Reversible and Irreversible Information Networks
IEEE Transactions on Information Theory
Linear Network Codes and Systems of Polynomial Equations
IEEE Transactions on Information Theory
Computing and communicating functions over sensor networks
IEEE Journal on Selected Areas in Communications
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We consider directed acyclic sum-networks with m sources and n terminals where the sources generate symbols from an arbitrary alphabet field F, and the terminals need to recover the sum of the sources over F. We show that for any co-finite set of primes, there is a sum-network which is linearly solvable only over fields of characteristics belonging to that set. We further construct a sum-network where a scalar linear solution exists over all fields other than the binary field F2. We also show that a sum-network is linearly solvable over a field if and only if its reverse network is linearly solvable over the same field.