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
Link To Document :
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