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On automorphisms of generalized algebraic-geometry codes

Authors: SPERA, Antonino Giorgio;

On automorphisms of generalized algebraic-geometry codes

Abstract

In coding theory, one often is interested in codes admitting large automorphism group. Certainly, the knowledge of the automorphism group of a code or even of part of this group gives information about the structure of the code and can allow to developing a decoding algorithm. In [IEEE Trans. Inform. Theory 45, No. 7, 2498--2501 (1999; Zbl 0956.94023)] \textit{C. Xing}, \textit{H. Niederreiter} and \textit{K. Y. Lam} introduced a construction of linear codes from algebraic function fields and places of degrees larger than one and called this construction generalized algebraic geometry codes. This kind of codes is a generalization of functional algebraic geometry codes and geometric Goppa codes. In the main part the author constructs automorphisms of generalized algebraic geometry codes from automorphisms of the underlying algebraic function field \(F/\mathbb F_q\). Furthermore, the author shows a connecting between automorphisms of generalized algebraic geometry codes and certain automorphism of the underlying algebraic function field and determines that the automorphism group of a generalized algebraic geometry code is a semidirect product under some hypothesis.

Country
Italy
Keywords

Algebra and Number Theory, Algebraic coding theory; cryptography (number-theoretic aspects), algebraic-geometry code, geometric Goppa codes, Geometric methods (including applications of algebraic geometry) applied to coding theory, generalized algebraic-geometry code

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Average
Top 10%
Average
hybrid
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