Some minimal cyclic codes over finite fields
Date of Issue2014
School of Physical and Mathematical Sciences
In this paper, the explicit expressions for the generating idempotents, check polynomials and the parameters of all minimal cyclic codes of length tpn over Fq are obtained, where p is an odd prime different from the characteristic of Fq, t and n are positive integers with t∣(q−1), gcd(t,p)=1 and View the MathML source. Our results generalize the main results in Pruthi and Arora (1997) and Arora and Pruthi (1999), which considered the cases t=1 and t=2 respectively. We propose an approach different from those in Pruthi and Arora (1997) and Arora and Pruthi (1999) to obtain the generating idempotents.
© 2014 Elsevier. This is the author created version of a work that has been peer reviewed and accepted for publication by Discrete Mathematics, 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.disc.2014.05.007].