Automorphism Groups of BWD-codes

In this paper we characterize the automorphism group of a particular class of irreducible cyclic codes by means of an important theorem of Carlitz and McConnel. The BWD-codes (balanced weight distribution) have the remarkable property that each nonzero weight appears with the same multiplicity. We also show that an irreducible cyclic BWD-code withNnonzero weights is a subscheme withNclasses of the Hamming scheme isomorphic to a cyclotomic scheme.