Automorphisms of hyperelliptic GAG-codes

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 2006 Italy English Publisher:Elsevier BVJournal:Electronic Notes in Discrete Mathematics, volume 26, pages 123-130 (issn: 1571-0653,

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Authors: PICONE, Alberto; SPERA, Antonino Giorgio;

doi: 10.1016/j.endm.2006.08.022 , 10.1016/j.disc.2007.12.013

handle: 10447/28577 , 10447/40120

Automorphisms of hyperelliptic GAG-codes

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Abstract

Generalized algebraic-geometry codes are linear codes which generalize the well-known geometric Goppa codes, since their construction makes use of places which are not necessarily of degree one. In this paper authors determine the \(n\)-automorphism group of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic function fields. Such group is, up to isomorphism, a subgroup of the automorphism group of the underlying function field. Further they calculate some examples of \(q\)-ary linear codes for \(q=5\), 7 in the hyperelliptic case. These examples show that it is possible to construct generalized algebraic-geometry codes with a nontrivial \(n\)-automorphism group.

Country

Italy

Related Organizations

National Institute for Nuclear Physics
Italy
Università degli studi di Salerno
Italy
University of Palermo
Italy

Keywords

Geometric Goppa codes ; generalized algebraic-geometry codes ; algebraic function fields ; automorphisms ; finite fields, Algebraic function fields, Automorphisms, Algebraic coding theory; cryptography (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry, Theoretical Computer Science, Generalized algebraic-geometry codes, geometric Goppa codes; finite fields; algebraic function fields; generalized algebraic geometry codes., Finite fields, Discrete Mathematics and Combinatorics, algebraic function fields, Geometric Goppa codes, geometric Goppa codes, Geometric methods (including applications of algebraic geometry) applied to coding theory, generalized algebraic-geometry codes

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