New lower bounds on q-ary error-correcting codes

Let A(q) (n, d) denote the maximum size of a q-ary code with length n and minimum distance d. For most values of n and d, only lower and upper bounds on A(q) (n, d) are known. In this paper new lower bounds on and updated tables of A(q) (n, d) for q is an element of {3, 4, 5} are presented. The new bounds are obtained through an extensive computer search for codes with prescribed groups of automorphisms. Groups that act transitively on the (coordinate,value) pairs as well as groups with certain other closely related actions are considered.