DocumentCode
1086196
Title
Systematic encoding via Grobner bases for a class of algebraic-geometric Goppa codes
Author
Heegard, Chris ; Little, John ; Saints, Keith
Author_Institution
Sch. of Electr. Eng., Cornell Univ., Ithaca, NY, USA
Volume
41
Issue
6
fYear
1995
fDate
11/1/1995 12:00:00 AM
Firstpage
1752
Lastpage
1761
Abstract
Any linear code with a nontrivial automorphism has the structure of a module over a polynomial ring. The theory of Grobner bases for modules gives a compact description and implementation of a systematic encoder. We present examples of algebraic-geometric Goppa codes that can be encoded by these methods, including the one-point Hermitian codes
Keywords
Goppa codes; algebraic geometric codes; linear algebra; linear codes; polynomials; Grobner bases; algebraic-geometric Goppa codes; linear code; modules; nontrivial automorphism; one-point Hermitian codes; polynomial ring; systematic encoding; Encoding; Galois fields; Linear algebra; Linear code; Mathematics; Polynomials;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.476247
Filename
476247
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