Why no cod farming?

I was reading something about the declining cod stocks all over the Atlantic. No one can agree on catch limits or anything that would preserve the cod.

Without getting into too much debate over catch limits and some of the criticism of fish farming in general, why can’t cod be farmed? What makes one fish more conducive to farming than another?

PDF - http://www.nmfs.noaa.gov/mb/sk/pdf/Report_18.pdf

Issues - National Geographic

Short answer - it is being farmed, but as with other fish-farming there are problems associated with the industry, particularly in terms of waste. Also farmed fish are still not identical in quality with wild caught.