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|Title:||Excellent nonlinear codes from algebraic function fields|
|Keywords:||Algebraic function fields|
Tsfasman-Vlǎduţ-Zink (TVZ) bound
|Source:||Stichtenoth, H., Xing, C. (2005-11). Excellent nonlinear codes from algebraic function fields. IEEE Transactions on Information Theory 51 (11) : 4044-4046. ScholarBank@NUS Repository. https://doi.org/10.1109/TIT.2005.856977|
|Abstract:||The Gilbert-Varshamov (GV) bound for asymptotic families of codes over F, has been improved by Tsfasman, Vlädug, and Zink (TVZ) in 1982, and only recently further improvements have been obtained by Xing, Elkies, and Niederreiter-Ozbudak, 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. © 2005 IEEE.|
|Source Title:||IEEE Transactions on Information Theory|
|Appears in Collections:||Staff Publications|
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