DocumentCode
1253335
Title
Partial geometric codes
Author
Pretzel, Oliver
Author_Institution
Dept. of Math., Imperial Coll. of Sci., Technol. & Med., London, UK
Volume
45
Issue
7
fYear
1999
fDate
11/1/1999 12:00:00 AM
Firstpage
2506
Lastpage
2512
Abstract
We present a theory of partial geometric Goppa (1981) codes, which can be applied to curves for which the genus is not explicitly known. That is often the case if the curve is nonsmooth or nonplanar. The only algebraic geometry required is familiarity with the basic concepts. Yet we are able to give a full account of all one-point codes including their error processors. We are also able to give a completely explicit construction for the initial code in a good sequence of codes based on a set of curves introduced by Garcia and Stichtenoth (Acad. Sci., Paris, vol.322 I, p.1067-70, 1996), for which the genus has not been determined
Keywords
Goppa codes; algebraic geometric codes; algebraic geometry; code sequence; curve genus; error processors; explicit construction; initial code; nonplanar curve; nonsmooth curve; one-point codes; partial geometric Goppa codes; Books; Code standards; Cost accounting; Geometry; Mathematics;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.796392
Filename
796392
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