DocumentCode
1086129
Title
Improved geometric Goppa codes. I. Basic theory
Author
Feng, Gui-Liang ; Rao, T.R.N.
Author_Institution
Center for Adv. Comput. Studies, Univ. of Southwestern Louisiana, Lafayette, LA, USA
Volume
41
Issue
6
fYear
1995
fDate
11/1/1995 12:00:00 AM
Firstpage
1678
Lastpage
1693
Abstract
In this paper, we present a construction of improved geometric Goppa codes which, for the case of r<2g, are often more efficient than the current geometric Goppa codes derived from some varieties, which include algebraic curves, hyperplanes, surfaces, and other varieties. For the special case of a plane in a three-dimensional projective space, the improved geometric Goppa codes are reduced to linear multilevel codes. For these improved geometric Goppa codes, a designed minimum distance can be easily determined and a decoding procedure which corrects up to half the designed minimum distance is also given
Keywords
Goppa codes; algebraic geometric codes; decoding; linear codes; decoding procedure; designed minimum distance; geometric Goppa codes; improved codes; linear multilevel codes; three-dimensional projective space; Decoding; Equations; Error correction codes; Helium; Linear algebra; Linear code; Parity check codes; Reed-Solomon codes; Voting;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.476241
Filename
476241
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