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FGLM-Like Decoding: from Fitzpatrick’s Approach to Recent Developments

In: Gröbner Bases, Coding, and Cryptography

Author

Listed:
  • Eleonora Guerrini

    (University of Trento, Department of Mathematics)

  • Anna Rimoldi

    (University of Trento, Department of Mathematics)

Abstract

Many decoding problems in algebraic coding theory can be solved by the computation of a suitable Gröbner basis. The Gröbner basis can often be computed via the FGLM algorithm or a related algorithm (like the Buchberger–Möller algorithm). In this tutorial we describe how this has been done in the literature from a historical point of view, starting from Fitzpatrick’s seminal 1995 paper, and covering recent developments for list decoding.

Suggested Citation

  • Eleonora Guerrini & Anna Rimoldi, 2009. "FGLM-Like Decoding: from Fitzpatrick’s Approach to Recent Developments," Springer Books, in: Massimiliano Sala & Shojiro Sakata & Teo Mora & Carlo Traverso & Ludovic Perret (ed.), Gröbner Bases, Coding, and Cryptography, pages 197-218, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-93806-4_12
    DOI: 10.1007/978-3-540-93806-4_12
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