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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Official URL: http://dx.doi.org/10.1109/TIT.2005.856977


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
ID Code:580
Deposited By:Henning Stichtenoth
Deposited On:28 Dec 2005 02:00
Last Modified:25 May 2011 14:05

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