  Linear network coding transmits information in terms of a basis of a vector
space and the information is received as a basis of a possible altered
vectorspace. Ralf Koetter and Frank R. Kschischang in Coding for errors and
erasures in random network coding (IEEE Transactions on Information Theory,
vol.54, no.8, pp. 3579-3591,2008) introduced a metric on the set af
vector-spaces and showed that a minimal distance decoder for this metric
achieves correct decoding if the dimension of the intersection of the
transmitted and received vector-space is sufficiently large. From the Veronese
varieties we construct explicit families of vector-spaces of constant dimension
where any pair of distinct vector-spaces are equidistant in the above metric.
The parameters of the resulting linear network codes which have maximal
error-protection are determined.
