Inequivalent cyclic codes of prime length

A characterization of the equivalence classes of prime-length cyclic codes over any finite field is given, generalizing the binary case solved by Leon, Masely, and Pless. In the special case of cyclic (p, k) codes over GF (q) , with P|(q - 1) , a one-to-one correspondence between the equivelance classes and the orbits of k -sets under the affine group, GA (1, p) is established.