title   
  

Excellent nonlinear codes from algebraic function fields

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

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
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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