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The cable that I use is a "30-foot DVI-D to DVI-D cable" with a 12-inch adapter (MiniDisplayport-to-DVI) to connect it to my iMac. And, just now, I tried an alternate single 25-foot cable (miniDisplayPort - to - DVI), but nothing changed; I still have the intermittent bright flashes.

http://www.datapro.net/techinfo/dvi_info.html

The official DVI specification mandates that all DVI equipment must maintain a signal at 5 meters (16 feet) in length. But many manufacturers are putting out much stronger cards and bigger monitors, so the maximum length possible is never exact.

Although the mandated DVI spec is 5 meters, we do carry cables up to 25 feet, and have succesfully extended them even longer than that (although results do vary depending on hardware). For guaranteed signal quality on long runs, you should consider using a powered DVI signal booster.
 
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