Although I'm new to this forum - I'm not new to electricity. UB might remember my old handle from Cannab . com etc.
I use 1k digitals with cool tubes. (several of them)
The cords they send out even from the factory arent worth a crap. As for a 16g feed to a 1k'r - no go. 16g wire is rated ~8-10 amps (amps x volts = watts).. Anywho long story short, you never want to exceed about 80% of the max it's rated for. So your 1kw light is likely pulling somewhere around 1100w minimum if its a magnetic, my digis are very efficient and only pull 1050..
I 'had' 16g computer style cables that came with mine, and I noticed they were getting warm (they were only 3-4' long),, if it GETS warm it can burn, and also if it's warm that means your 1) wasting electricity 2) exceeding the carrying capacity of the wire.
I went with 14g plugs for my ballasts/lights - they now are nice and cool and actually use LESS power.. *I had to go with 14g only because it's the biggest I could find* You can find 14awg cords for like servers and such (they pull alot of power). Also the shorter the better. My 14g cables are rated at 15amps. (15x120 = 1800) *.8 = 1440 (so a cpl hundred watts overage)
Most computer cables however are stranded 18/16g. FWIW: In stranded wiring you need a little bigger size vs solid wire. Just remember - it's NOT what it 'CAN' do it's what it's SAFE to do =)