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A New Construction of Algebraic Geometry Codes

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

We present a new construction of linear codes based on algebraic geometry. An important feature of this construction is that we can use places of arbitrary degree and not just rational places as in Goppa's construction. Examples show that this leads to various improvements on Goppa's construction.

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Authors and Affiliations

  1. Institute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, A-1010 Vienna, Austria (e-mail: niederreiter@oeaw.ac.at), , , , , , AT

    Harald Niederreiter

  2. Department of Mathematics, The National University of Singapore, Lower Kent Ridge Road, Singapore 119260 (e-mail: xingcp@comp.nus.edu.sg), , , , , , SG

    Chaoping Xing

  3. School of Computing, The National University of Singapore, Lower Kent Ridge Road, Singapore 119260 (e-mail: lamky@comp.nus.edu.sg), , , , , , SG

    Kwok Yan Lam

Authors
  1. Harald Niederreiter
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  2. Chaoping Xing
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  3. Kwok Yan Lam
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Received: September 18, 1998

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Niederreiter, H., Xing, C. & Lam, K. A New Construction of Algebraic Geometry Codes. AAECC 9, 373–381 (1999). https://doi.org/10.1007/s002000050111

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  • DOI: https://doi.org/10.1007/s002000050111