DocumentCode
1490794
Title
On the splitting of places in a tower of function fields meeting the Drinfeld-Vladut bound
Author
Aleshnikov, Ilia ; Kumar, P. Vijay ; Shum, Kenneth W. ; Stichtenoth, Henning
Author_Institution
Univ. Gesamthochschule Essen, Germany
Volume
47
Issue
4
fYear
2001
fDate
5/1/2001 12:00:00 AM
Firstpage
1613
Lastpage
1619
Abstract
A description of how places split in an asymptotically optimal tower of function fields studied by Garcia and Stichtenoth (1995) is provided and an exact count of the number of places of degree one is given. This information is useful in the setting up of generator matrices for algebraic-geometry codes constructed over this function field tower. These long codes have performance that asymptotically improves upon the Gilbert-Varshamov bound
Keywords
algebraic geometric codes; matrix algebra; Drinfeld-Vladut bound; Gilbert-Varshamov bound; algebraic-geometry codes; asymptotically optimal tower; function field tower; function fields; generator matrices; long codes; places splitting; Codes; Cryptography; Decoding; Equations; Galois fields; Interpolation; Linear systems; Notice of Violation; Poles and towers; Polynomials;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.923746
Filename
923746
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