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International Conference on Theory and Applications of Models of Computation

TAMC 2012: Theory and Applications of Models of Computation pp 295–306Cite as

Stopping Set Distributions of Algebraic Geometry Codes from Elliptic Curves

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7287))

Abstract

The stopping sets and stopping set distribution of a binary linear code play an important role in the iterative decoding of the linear code over a binary erasure channel. In this paper, we study stopping sets and stopping distributions of some residue algebraic geometry (AG) codes. For the simplest AG code, i.e., generalized Reed-Solomon code, it is easy to determine all the stopping sets. Then we consider AG codes from elliptic curves. We use the group structure of rational points of elliptic curves to present a complete characterization of stopping sets. Then the stopping sets, the stopping set distribution and the stopping distance of the AG code from an elliptic curve are reduced to the search, computing and decision versions of the subset sum problem in the group of rational points of the elliptic curve, respectively.

The first two authors are supported by the National Natural Science Foundation of China (Nos. 61171082, 10990011 and 60872025).

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Author information

Authors and Affiliations

  1. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, China

    Jun Zhang & Fang-Wei Fu

  2. Department of Mathematics, University of California, Irvine, CA, 92697-3875, USA

    Daqing Wan

Authors
  1. Jun Zhang
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  2. Fang-Wei Fu
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  3. Daqing Wan
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Resource Planning and Generation, Indian Institute of Technology Kanpur, 208016, Kanpur, India

    Manindra Agrawal

  2. Department of Pure Mathematics, Leeds, University of Leeds, LS2 9JT, UK

    S. Barry Cooper

  3. Institute of Software, Chinese Academy of Sciences, P.O. Box 8718, 100190, Beijing, P.R. China

    Angsheng Li

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Zhang, J., Fu, FW., Wan, D. (2012). Stopping Set Distributions of Algebraic Geometry Codes from Elliptic Curves. In: Agrawal, M., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2012. Lecture Notes in Computer Science, vol 7287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29952-0_31

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  • DOI: https://doi.org/10.1007/978-3-642-29952-0_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29951-3

  • Online ISBN: 978-3-642-29952-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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