The explicit expressions for the 2n+1 primitive idempotents in R_pⁿ = F[x]/< x^pⁿ -1>, where F is the field of prime power order q and the multiplicative order of q modulo pⁿ is ø(pⁿ)/2(n≥1 and p is an odd prime), are obtained. An algorithm for computing the generating polynomials of the minimal QR cyclic codes of length pⁿ, generated by these primitive idempotents, is given and hence some bounds on the minimum distance of some QR codes of prime length over GF(q)(q=2, 3, ...) are obtained. AMS Mathematics Subject Classification : 94B15, 16534, 20C05