I have a rough concrete slab roughly 10x10. My question is can I build a wood deck over this? The space between the bottom of the door to the top of the slab would only allow me to use a 2x6 as a ledger and 2x4's as joists. If I space the 2x4's closer together then normal will this work. I plan on building the deck just longer than the slab so I can put two 4x4's in the corners opposite the house. Thank you.

A bearing deck would have it's joists laid directly on top of the slab (these are called sleepers). Normally, a slab is not level (for drainage purposes). Therefore, the bottom of each joist for the deck needs to be cut at the angle of the slab to make the deck level. Posts or other support are not normally needed in this case. The joists would be attached by a perimeter board called a band board. I would lay 15 lb. roofing felt down on the slab.

You could put the legs into those concrete leg holders that would rest directly on the slab. This would prevent rot to the bottom of the posts.