The Poincaré Polynomial of a Linear Code

Galindo, Carlos; Hernando, Fernando; Monserrat, Francisco; Pellikaan, Ruud

Por favor, use este identificador para citar o enlazar este ítem:http://uvadoc.uva.es/handle/10324/36079

Título

The Poincaré Polynomial of a Linear Code

Autor

Año del Documento

2018

Editorial

Springer Link

Descripción

Producción Científica

Documento Fuente

Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics (Festschrift for Antonio Campillo on the Occasion of his 65th Birthday), 2018, p. 525-535

Abstract

We introduce the Poincar´e polynomial of a linear q-ary code and its relation to the corresponding weight enumerator. We prove that the Poincar´e polynomial is a complete invariant of the code in the binary and ternary case and it is not when q ≥ 4. Finally we determine this polynomial for MDS codes and, by means of a recursive formula, for binary Reed-Muller codes.

Palabras Clave

Poincaré Polynomial

Polinomio de Poincaré

Linear code

Código lineal

ISBN

978-3-319-96827-8

Version del Editor

https://link.springer.com/chapter/10.1007/978-3-319-96827-8_23