The weight distribution of some irreducible cyclic codes

Let Fq be the finite field with q elements, p be an odd prime co-prime to q and m⩾1 be an integer. In this paper, we explicitly determine the weight distribution of all the irreducible cyclic codes of length pm over Fq from their generating polynomials in three different cases, when (i) the multiplicative order of q modulo pm is ϕ(pm), (ii) the multiplicative order of q modulo pm is a power of p, and (iii) the multiplicative order of q modulo pm is twice a power of p.