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On the Construction of Some Optimal Polynomial Codes

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Computational Intelligence and Security (CIS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3802))

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Abstract

We generalize the idea of constructing codes over a finite field F q by evaluating a certain collection of polynomials at elements of an extension field of F q . Our approach for extensions of arbitrary degrees is different from the method in [3]. We make use of a normal element and circular permutations to construct polynomials over the intermediate extension field between F q and F \(_{q^{t}}\) denoted by F \(_{q^{s}}\) where s divides t. It turns out that many codes with the best parameters can be obtained by our construction and improve the parameters of Brouwer’s table [1]. Some codes we get are optimal by the Griesmer bound.

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References

  1. Brouwer, A.E.: Bounds on the Minimum Distance of Linear Codes (on-line server), http://www.win.tue.nl/~aeb/voorlincod.html

  2. Xing, C., Ling, S.: A Class of Linear Codes with Good Parameters. IEEE Trans. Inform. Theory 46, 2184–2188 (2000)

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Information Engineering University, P.O. Box 1001-7410, Zhengzhou, 450002, China

    Yajing Li & Weihong Chen

Authors
  1. Yajing Li
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  2. Weihong Chen
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Editor information

Editors and Affiliations

  1. Microelectronic Instiute, Xidian University, 710071, Xi’an, China

    Yue Hao

  2. Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Jiming Liu

  3. School of Computer Science and Technology, Xidian University, Xi’an, China

    Yu-Ping Wang

  4. Department of Computer Science, Hong Kong Baptist University, Hong Kong,  

    Yiu-ming Cheung

  5. School of Electrical and Electronic Engineering, University of Manchester, UK

    Hujun Yin

  6. Life Science Research Center, School of Electronic Engineering, Xidian University, 710071, Xi’an, Shaanxi, China

    Licheng Jiao

  7. Key Laboratory of Computer Networks and Information Security(Ministry of Education), Xidian University, 710071, Xi’an, China

    Jianfeng Ma

  8. National Laboratory of Antennas and Microwave Technology, Xidian University, 710071, Xi’an, Shanxi, P.R. China

    Yong-Chang Jiao

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© 2005 Springer-Verlag Berlin Heidelberg

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Li, Y., Chen, W. (2005). On the Construction of Some Optimal Polynomial Codes. In: Hao, Y., et al. Computational Intelligence and Security. CIS 2005. Lecture Notes in Computer Science(), vol 3802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11596981_11

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  • DOI: https://doi.org/10.1007/11596981_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30819-5

  • Online ISBN: 978-3-540-31598-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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