Excellent nonlinear codes from algebraic function fields

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Stichtenoth, Henning and Xing, Chaoping P. (2005) Excellent nonlinear codes from algebraic function fields. IEEE Transactions On Information Theory, 51 (11). pp. 4044-4046. ISSN 0018-9448

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Abstract

The Gilbert-Varshamov (GV) bound for asymptotic families of codes over F/sub q/ has been improved by Tsfasman, Vla/spl breve/dut$80, and Zink (TVZ) in 1982, and only recently further improvements have been obtained by Xing, Elkies, and Niederreiter-O/spl uml/zbudak, by considering also nonlinear codes. These improvements involve higher derivations in function fields and are very computational. We give in this correspondence a much simpler proof for those improvements. Our construction of asymptotically good nonlinear codes is very similar to Goppa's construction of algebraic-geometry codes.
Item Type: Article
Uncontrolled Keywords: algebraic function fields; algebraic-geometry codes; asymptotic bounds; Tsfasman-Vladut-Zink (TVZ) bound
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Henning Stichtenoth
Date Deposited: 28 Dec 2005 02:00
Last Modified: 26 Apr 2022 08:10
URI: https://research.sabanciuniv.edu/id/eprint/580

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