The Code of Vengeance was a set of Andorian laws that allowed for personal combat.
It can only be invoked in regards to personal grievances on the assumption that the right person will win. A duel is only appropriate between the aggrieved party and the alledged perpetrator which means that only those two may participate. The code mandates a single duel for each crime in order to prevent an Andorian from facing several members of the same family over the same accusation. Once a duel settles the matter, it is considered closed.
Other rules permit satisfaction to the first strike, the first blood or until a participant yields and entirely depends upon the nature of the dispute. However, the most grievous violations to personal freedoms such as the death of a loved one results in a fight to the death.
Typically, Andorians reserve the code for other Andorians and only traditionalists call out members of other species to fight under these rules. Starfleet stringently discourages the practice, even among Andorian crew members. (Decipher RPG module: Aliens)