You know there is actually a link to a Coach site called a Drilldown and you can put in the last numbers in the serial number and a picture of the hand bag will show up. The picture of the handbag that shows up is the one that the actual serial number belongs to..
If the bag does not have a serial number, it might still be real, but it could just be an older model. Fake Coach bags will often have irregular stitching, breaks or misalignment in the Coach pattern, or inferior materials.
Where it says '3577' just replace it with the last numbers in the Code. I found this link when I began searching for Coach on Ebay. It really helped me kind of weed out the fakes and the authentic Coaches. It doesn't work for every purse but then that's when I would start questioning the seller. Hope that this helps some for those searching for authentic Coaches. If this has been brought up before.