The Knights' code of chivalry, according to Sir Thomas Malory (This is specified for the knights of the round table):
“Sir Thomas Malory: Le morte D’Arthur
Upon this covenant could you become a member of the round table, with, of course, the approval of the King.
The round table knew two kings (two kings who "were in command of it", so to speak. There were other kings though, who served as knights at the court of King arthur. For example: King pellinore): King Arthur and King Leodegrance (who was the father of queen guenevere).
King Constantine, who ruled after Arthur's death (=Le morte D'arthur), was not given the round table because it simply did not exist anymore. It had fallen apart during the quest for the Holy Sangreal (Holy Grail), because of the many knights that died during their travels in search of the Grail.
reference: Le Morte D'Arthur, by Sir Thomas Malory