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.
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CITATION STYLE
Galindo, C., Hernando, F., Monserrat, F., & Pellikaan, R. (2018). The Poincaré polynomial of a linear code. In Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics: Festschrift for Antonio Campillo on the Occasion of his 65th Birthday (pp. 525–535). Springer International Publishing. https://doi.org/10.1007/978-3-319-96827-8_23
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