Automorphisms and Encoding of AG and Order Domain Codes [chapter]

John B. Little
2009 Gröbner Bases, Coding, and Cryptography  
We survey some encoding methods for AG codes, focusing primarily on one approach utilizing code automorphisms. If a linear code C over 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 P. 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.
doi:10.1007/978-3-540-93806-4_7 fatcat:nzs6cqo33baivdsv6zp6omamwa