The Poincaré Polynomial of a Linear Code
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comunitat-uji-handle3:10234/146078
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Title
The Poincaré Polynomial of a Linear CodeAuthor (s)
Date
2018-09-19Publisher
SpringerISBN
978-3-319-96826-1; 978-3-319-96827-8 (online)Bibliographic citation
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, ChamType
info:eu-repo/semantics/bookPartPublisher version
https://link.springer.com/chapter/10.1007/978-3-319-96827-8_23Version
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Abstract
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. [-]
Investigation project
Spanish Ministry of Economy/FEDER (grants MTM2015-65764-C3-2-P and MTM2015-69138-REDT) ; University Jaume I (grant PB1-1B2015-02. 1)Rights
© 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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