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Excellent nonlinear codes from algebraic function fields

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2 Author(s)
Stichtenoth, H. ; Dept. of Math., Univ. of Duisburg-Essen, Essen, Germany ; Chaoping Xing

The Gilbert-Varshamov (GV) bound for asymptotic families of codes over Fq has been improved by Tsfasman, Vla˘dut$80, and Zink (TVZ) in 1982, and only recently further improvements have been obtained by Xing, Elkies, and Niederreiter-Özbudak, 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.

Published in:

Information Theory, IEEE Transactions on  (Volume:51 ,  Issue: 11 )

Date of Publication:

Nov. 2005

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