Minimal Cyclic Codes of Length 2pn

In this paper we completely describe the 2n+2 minimal cyclic codes of length 2pnoverFq, as minimal ideals in the ringR=Fq[x]/ x2pn−1 in terms of their generating idempotents. Explicit expressions for the primitive idempotents, generating polynomials, minimum distance, and dimension of these codes are obtained. We assume thatFq=GF(q), whereq(prime power) is primitive root modulo 2pnandn≥1 is an integer, and bothpandqare odd.