A note on the weight distribution of some cyclic codes

Let F-q be the finite field with q elements and C-n be the cyclic group of order n, where n is a positive integer relatively prime to q. Let H, K be subgroups of C-n such that H is a proper subgroup of K. In this note, the weight distributions of the cyclic codes of length n over F-q with generating idempotents (K) over cap and e(II,K) = (H) over cap - (K) over cap are explicitly determined, where (K) over cap = 1/vertical bar K vertical bar Sigma(g is an element of K) g and (H) over cap = 1/vertical bar H vertical bar Sigma(g is an element of H) g. Our result naturally gives a new characterization of a theorem by Sharma and Bakshi [18] that determines the weight distribution of all irreducible cyclic codes of length p(m) over F-q, where p is an odd prime and q is a primitive root modulo p(m). Finally, two examples are presented to illustrate our results. (C) 2015 Elsevier Inc. All rights reserved.