Generalized AG codes and generalized duality

Authors:
Gerhard Dorfer;Hiren Maharaj
Affiliations:
Department of Algebra and Computational Mathematics, Vienna University of Technology, Wiedner Hauptstr. 8-10/118, A-1040 Vienna, Austria and Institute of Discrete Mathematics, Austrian Academy of ...;Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA
Venue:
Finite Fields and Their Applications
Year:
2003

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Abstract

In (J. Pure Appl. Algebra 55 (1988) 199), Stichtenoth gave sufficient conditions for algebraic-geometric Goppa codes to be self-dual. We adapt this work using differentials to the setting of generalized AG codes introduced by Xing et al. (IEEE Trans. Inform. Theory 45 (1999) 2498). As a consequence we are naturally led to generalized notions of duality for codes. Many examples are presented.