Linear Network Codes and Systems of Polynomial Equations

If and are nonnegative integers and F is a field, then a polynomial collection {p1, . . . , p} Z[1, . . . , ] is said to be solvable over F if there exist 1, . . . , F such that for all i = 1, . . . , we have pi(1, . . . , ) = 0. We say that a network and a polynomial collection are solvably equivalent if for each field F the network has a scalar-linear solution over F if and only if the polynomial collection is solvable over F. Koetter and M

• Type: Journal
• Year: 2008
• Where: TIT
• Authors: Randall Dougherty, Christopher F. Freiling, Kenneth Zeger
• Keywords: Acyclic Network, Nonnegative Integers, Polynomial Collection, TIT 2008