Minimal Codes of Prime-Power Length

Explicit expressions for the (n+ 1) primitive idempotents inFG(the group algebra of the cyclic groupGof orderpn(podd prime,n> 1) over the finite fieldFof prime power orderqwhereqis a primitive root modulopn) are obtained. The minimum distance, the dimension, and the generating polynomial of the (n+ 1) minimum codes generated by the primitive idempotents are also obtained.