A note on the weight distribution of some cyclic codes

Abstract

Let Fq be the finite field with q elements and Cn be the cyclic group of order n, where n is a positive integer relatively prime to q . Let H,K be subgroups of Cn such that H is a proper subgroup of K. In this note, the weight distributions of the cyclic codes of length n over Fq with generating idempotents View the MathML source and View the MathML source are explicitly determined, where View the MathML source and View the MathML source. 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 pm over Fq, where p is an odd prime and q is a primitive root modulo pm. Finally, two examples are presented to illustrate our results.