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According to the proof, it looks like if the outer code is Reed Solomon of rate R, then the rate of Justesen code is R/2 and the distance is >(1-R-\eps)*H^{-1}(1/2 - \eps).
Note that in the case the distance of the code is >(1-2r-\eps)*H^{-1}(1/2 - \eps), where r is the rate of the Justesen code. This contradict the box on the right.
Do I miss something?
What is \epsilon? How does it depend on other code parameters?