Perfect codes in SL(2,2f)

It is shown that any subset X which is closed under conjugation does not divide SL(2,2f) non-trivially if f≠1; that is, there exists no perfect code in the Cayley graph of SL(2,2f) with respect to X if f≠1. A list of subsets X closed under conjugation and natural numbers λ such that X possibly divides λSL(2,2f) has been established. Moreover, as a case where X is not closed under conjugation, the orbits X of involutions by conjugation of a Singer cycle of SL(2,2f) have been considered and it has been determined whether they divide λSL(2,2f) non-trivially or not.