I went a little more in-depth about how manufacturer coupons work in a comment above. Long story short there isn’t any “server side” verification. As long as you have the correct format, anyone can create a barcode that will scan and give you the offer you encoded. But you will be committing fraud (don’t do it) and it does get checked.

There isn’t a central db of valid coupons, the discount and product barcode are encoded in the coupon barcode