I suggest reading Page 33 of the Manual, which explains how the airline codes are used for. They enter into play only as "tie-breakers" when there are multiple operators allowed on the airport at the same score, according to the the internal scoring rules.
So, for example, if one airport you have, let's say, American Airlines and United as possible candidates at the same scoring, normally any gate would give you a choice between those two. But if there are some gate with the AA or AAL codes, American will get a scoring boost, and will "beat" United at that gate. In this case, American being the only one left, will be selected even without a menu, since it was the only possible choice.
Swedavia code is just...Swedavia, the 3 letter code limitation is only when those codes are read from the airport, but when you write them yourself, they can be anything. You can find the codes in the \Addon Manager\texture\rules_handing.cfg file.
