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Journal article

Construction and decoding of a class of algebraic geometry codes

By Justesen, Jørn1; Larsen, Knud J.1; Jensen, Helge Elbrønd2; Havemose, Allan3; Høholdt, Tom2

From

Department of Telecommunication, Technical University of Denmark1

Department of Mathematics, Technical University of Denmark2

Technical University of Denmark3

A class of codes derived from algebraic plane curves is constructed. The concepts and results from algebraic geometry that were used are explained in detail; no further knowledge of algebraic geometry is needed. Parameters, generator and parity-check matrices are given. The main result is a decoding algorithm which turns out to be a generalization of the Peterson algorithm for decoding BCH decoder codes

Language: English
Publisher: IEEE
Year: 1989
Pages: 811-821
ISSN: 15579654 and 00189448
Types: Journal article
DOI: 10.1109/18.32157
ORCIDs: Larsen, Knud J.
Keywords

Buildings Circuit theory Decoding Equations Galois fields Geometry Machinery Parity check codes Peterson algorithm Polynomials Reed-Solomon codes algebraic geometry codes algebraic plane curves code construction codes decoding generator matrices parity-check matrices

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