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Equidistant binary arithmetic codes

Let C(B) denote the binary cyclic AN code with generator A , where AB=2^{n} - 1 . It is known that C(B) is equidistant if B is a prime power p^{k} , where either 2 or -2 is primitive modulo B provided p\equiv 1 \pmod{3}{\rm if} k > 1 . It is conjectured that these are the only B such that C(B) is equidistant. We have verified this for B . Several results are established that further limit the possibilities for counterexamples to the conjecture.