Some codes in symmetric and linear groups.

For a finite group G , a positive integer λ , and subsets X , Y of G , write λ G = X Y if the products x y (x ∈ X , y ∈ Y), cover G precisely λ times. Such a subset Y is called a code with respect to X , and when λ = 1 it is a perfect code in the Cayley graph Cay (G , X). In this paper we present various families of examples of such codes, with X closed under conjugation and Y a subgroup, in symmetric groups, and also in special linear groups S L 2 (q). We also propose conjectures about the existence of some much wider families. [ABSTRACT FROM AUTHOR]