The Poincaré polynomial of a linear code

Carlos Galindo, Fernando Hernando, Franciso Montserrat, G.R. Pellikaan

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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 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.

Original languageEnglish
Title of host publicationSingularities, Algebraic Geometry, Commutative Algebra, and Related Topics
Subtitle of host publicationFestschrift for Antonio Campillo on the Occasion of his 65th Birthday
EditorsGert-Martin Greuel, Luis Narváez Macarro, Sebastià Xambó-Descamps
Place of PublicationCham
PublisherSpringer
Chapter23
Pages525-535
Number of pages11
ISBN (Electronic)978-3-319-96826-1
ISBN (Print)978-3-319-96827-8
DOIs
Publication statusPublished - 18 Sep 2018

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