The Poincaré Polynomial of a Linear Code

Carlos Galindo (), Fernando Hernando (), Francisco Monserrat () and Ruud Pellikaan ()
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Carlos Galindo: Universitat Jaume I, Departamento de Matemáticas, Instituto Universitario de Matemáticas y Aplicaciones de Castellón
Fernando Hernando: Universitat Jaume I, Departamento de Matemáticas, Instituto Universitario de Matemáticas y Aplicaciones de Castellón
Francisco Monserrat: Universidad Politécnica de Valencia, Instituto Universitario de Matemática Pura y Aplicada (IUMPA)
Ruud Pellikaan: Technische Universiteit Eindhoven, Discrete Mathematics

A chapter in Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics, 2018, pp 525-535 from Springer

Abstract: 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 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-96827-8_23

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DOI: 10.1007/978-3-319-96827-8_23

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