Irreducible cyclic codes of length 2pn

Let q be an odd prime power and p be an odd prime with gcd(p, q) = 1. Let the order of q modulo p be f and gcd (p-1/f, q) = 1. Here explicit expressions for all the primitive idempotents in the ring R-2pn = GF(q)[x]/(x(2pn) - 1), for any positive integer n, are obtained in terms of cyclotomic numbers, provided p does not divide q(f)-1/2p, if n >= 2. Some lower bounds on the minimum distances of irreducible cyclic codes of length 2p(n) over GF(q) are also obtained.