Would you call this a paradox?

One definition of a paradox is "an apparently true statement or group of 
statements that leads to a contradiction or a situation which defies 
intuition"

Both Claude Shannon and Andrey Kolmogorov define the quantity of
information 
contained in a string in terms of the number of bits required to specify
the 
string.  This seems eminently reasonable -- the fewer the bits required to

specify a string, the less "information" it contains -- but it leads 
ineluctably to the conclusion that information is at its maximum in random

numbers.

Is it a contradiction to say that random numbers contain "information",
much 
less "maximum information"?  Is it counterintuitive?

Does it fit the definition of a paradox, in your opinion?