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On the Construction of Some Optimal Polynomial Codes

  • Yajing Li
  • Weihong Chen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3802)

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

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Yajing Li
    • 1
  • Weihong Chen
    • 1
  1. 1.Department of Applied MathematicsInformation Engineering UniversityZhengzhouChina

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