Sort of. You can always license your IP (code) how you want. However if you distribute the GPL code together with your product you can’t say the whole bundle is

Sort of. You can always license your IP (code) how you want. However if you distribute the GPL code together with your product you can’t say the whole bundle is BSD. (I understand you can dynamically link to GPL libraries distributed separately if you want that, but I’m not 100% sure where bundling .so/.DLL files leaves you).