Automorphisms and Encoding of AG and Order Domain Codes

John B. Little ()
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John B. Little: College of the Holy Cross, Department of Mathematics and Computer Science

A chapter in Gröbner Bases, Coding, and Cryptography, 2009, pp 107-120 from Springer

Abstract: 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.

Keywords: Linear Code; Cyclic Code; Hermitian Curve; Goppa Code; Order Domain (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-93806-4_7

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DOI: 10.1007/978-3-540-93806-4_7

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