The weight distribution of some irreducible cyclic codes

Let F(q) 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 p(m) over F(q) from their generating polynomials in three different cases, when (i) the multiplicative order of q modulo p(m) is phi(p(m)), (ii) the multiplicative order of q modulo p(m) is a power of p, and (iii) the multiplicative order of q modulo p(m) is twice a power of p. (C) 2011 Elsevier Inc. All rights reserved.