There's a million and one codes out there, all material specific, position specific, and welding medium specific. And that's just the tip of an iceberg. Fillet Welds, Butt welds. Plate or tube.. etc. etc.
On top of that, each company out there will require their own codings and WPQ (weld procedure qualification). Weld procedures will need to be written for the material you can weld, with limits on material thicknesses and the positions you can weld in. Then you will need to be 'qualified' to that specification by producin a witnessed test piece. After that, depending on the area of business, you be required to have your test piece sent to test engineer, for destructive and non detructive testing.
It's an absolute minefield, and you'd do well to read a copy of BS15614 or EN 287 or EN 288, but as a guide BS15614 will give you the info you need to start with.
I could witter on all day, but it's my job and I like to have a break..