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Automorphisms and Encoding of AG and Order Domain Codes

In: Gröbner Bases, Coding, and Cryptography

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  • John B. Little

    (College of the Holy Cross, Department of Mathematics and Computer Science)

Abstract

We survey some encoding methods for AG codes, focusing primarily on one approach utilizing code automorphisms. If a linear code C over $\mathbb{F}_{q}$ has a finite Abelian group H as a group of automorphisms, then C has the structure of a module over a polynomial ring ℘. This structure can be used to develop systematic encoding algorithms using Gröbner bases for modules. We illustrate these observations with several examples including geometric Goppa codes and codes from order domains.

Suggested Citation

  • John B. Little, 2009. "Automorphisms and Encoding of AG and Order Domain Codes," Springer Books, in: Massimiliano Sala & Shojiro Sakata & Teo Mora & Carlo Traverso & Ludovic Perret (ed.), Gröbner Bases, Coding, and Cryptography, pages 107-120, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-93806-4_7
    DOI: 10.1007/978-3-540-93806-4_7
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