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
fDate :
11/1/1995 12:00:00 AM
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;
Journal_Title :
Information Theory, IEEE Transactions on