Some minimal cyclic codes over finite fields
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 Vie...
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sg-ntu-dr.10356-998912023-02-28T19:41:51Z Some minimal cyclic codes over finite fields Hongwei, Liu Guanghui, Zhang Bocong, Chen School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Discrete mathematics 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. Accepted version 2014-08-21T02:38:42Z 2019-12-06T20:13:06Z 2014-08-21T02:38:42Z 2019-12-06T20:13:06Z 2014 2014 Journal Article Chen, B., Liu, H., & Zhang, G. (2014). Some minimal cyclic codes over finite fields. Discrete Mathematics, 331, 142-150. https://hdl.handle.net/10356/99891 http://hdl.handle.net/10220/20361 10.1016/j.disc.2014.05.007 180562 en Discrete mathematics © 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]. application/pdf |
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DRNTU::Science::Mathematics::Discrete mathematics Hongwei, Liu Guanghui, Zhang Bocong, Chen Some minimal cyclic codes over finite fields |
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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. |
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School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Hongwei, Liu Guanghui, Zhang Bocong, Chen |
| format |
Article |
| author |
Hongwei, Liu Guanghui, Zhang Bocong, Chen |
| author_sort |
Hongwei, Liu |
| title |
Some minimal cyclic codes over finite fields |
| title_short |
Some minimal cyclic codes over finite fields |
| title_full |
Some minimal cyclic codes over finite fields |
| title_fullStr |
Some minimal cyclic codes over finite fields |
| title_full_unstemmed |
Some minimal cyclic codes over finite fields |
| title_sort |
some minimal cyclic codes over finite fields |
| publishDate |
2014 |
| url |
https://hdl.handle.net/10356/99891 http://hdl.handle.net/10220/20361 |
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1759855337142222848 |