A note on the weight distribution of some cyclic codes
Date of Issue2015
School of Physical and Mathematical Sciences
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  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.
DRNTU::Science::Physics::Atomic physics::Field theories
Finite fields and their applications
© 2015 Elsevier. This is the author created version of a work that has been peer reviewed and accepted for publication by Finite Fields and Their Applications, Elsevier. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1016/j.ffa.2015.03.003].