The Poincaré Polynomial of a Linear Code
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Otros documentos de la autoría: Galindo, Carlos; Hernando, Fernando; Montserrat Delpalillo, Francisco José; Pellikaan, Ruud
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Título
The Poincaré Polynomial of a Linear CodeFecha de publicación
2018-09-19Editor
SpringerISBN
978-3-319-96826-1; 978-3-319-96827-8 (online)Cita bibliográfica
Galindo C., Hernando F., Monserrat F., Pellikaan R. (2018) The Poincaré Polynomial of a Linear Code. In: Greuel GM., Narváez Macarro L., Xambó-Descamps S. (eds) Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics. Springer, ChamTipo de documento
info:eu-repo/semantics/bookPartVersión de la editorial
https://link.springer.com/chapter/10.1007/978-3-319-96827-8_23Versión
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Resumen
We introduce the Poincaré polynomial of a linear q-ary code and its relation to the corresponding weight enumerator. The question of whether the Poincaré polynomial is a complete invariant is answered affirmatively ... [+]
We introduce the Poincaré polynomial of a linear q-ary code and its relation to the corresponding weight enumerator. The question of whether the Poincaré polynomial is a complete invariant is answered affirmatively for q = 2, 3 and negatively for q ≥ 4. Finally we determine this polynomial for MDS codes and, by means of a recursive formula, for binary Reed-Muller codes. [-]
Proyecto de investigación
Spanish Ministry of Economy/FEDER (grants MTM2015-65764-C3-2-P and MTM2015-69138-REDT) ; University Jaume I (grant PB1-1B2015-02. 1)Derechos de acceso
© Springer Nature Switzerland AG 2018. Reprinted by permission from Springer Nature: Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics (Galindo C., Hernando F., Monserrat F., Pellikaan R. (2018) The Poincaré Polynomial of a Linear Code. In: Greuel GM., Narváez Macarro L., Xambó-Descamps S. (eds) Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics. Springer, Cham), Copyright © Springer Nature Switzerland AG 2018, advance online publication: 19 September 2018, (https://doi.org/10.1007/978-3-319-96827-8_23)
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