Keywords
Linear function
Linear network coding
Linear rank inequality
Network capacity
How to Cite
Abstract
Network coding focuses on studying the transmission of messages through a directed graph or network in such a way that they are received by their intended receivers. It is of interest to determine the best way to transmit messages, which is measured by a rate. The inverse function method is a technique that involves the construction of linear functions that satisfy certain conditions associated with the topology in a network. Depending on the network structure, the method could succeed in producing an inequality inherent to linear algebra, which in turn provides information about the behavior of the rate with respect to a vector space over a finite field. This paper shows that the method can be used with the network known as Char-2, resulting in a valid inequality in vector spaces defined over odd-characteristic fields.
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