The Poincaré polynomial of a linear code

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

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

The Poincaré polynomial of a linear code

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

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Hoofdstuk › Academic › peer review

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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.

Originele taal-2	Engels
Titel	Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics
Subtitel	Festschrift for Antonio Campillo on the Occasion of his 65th Birthday
Redacteuren	Gert-Martin Greuel, Luis Narváez Macarro, Sebastià Xambó-Descamps
Plaats van productie	Cham
Uitgeverij	Springer
Hoofdstuk	23
Pagina's	525-535
Aantal pagina's	11
ISBN van elektronische versie	978-3-319-96826-1
ISBN van geprinte versie	978-3-319-96827-8
DOI's	https://doi.org/10.1007/978-3-319-96827-8_23
Status	Gepubliceerd - 18 sep. 2018

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

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Galindo, C., Hernando, F., Montserrat, F., & Pellikaan, G. R. (2018). The Poincaré polynomial of a linear code. In G.-M. Greuel, L. Narváez Macarro, & S. Xambó-Descamps (editors), Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics: Festschrift for Antonio Campillo on the Occasion of his 65th Birthday (blz. 525-535). Springer. https://doi.org/10.1007/978-3-319-96827-8_23

Galindo, Carlos ; Hernando, Fernando ; Montserrat, Franciso et al. / The Poincaré polynomial of a linear code. Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics: Festschrift for Antonio Campillo on the Occasion of his 65th Birthday. redacteur / Gert-Martin Greuel ; Luis Narváez Macarro ; Sebastià Xambó-Descamps. Cham : Springer, 2018. blz. 525-535

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title = "The Poincar{\'e} polynomial of a linear code",

abstract = "We introduce the Poincar{\'e} polynomial of a linear q-ary code and its relation to the corresponding weight enumerator. The question of whether the Poincar{\'e} 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.",

author = "Carlos Galindo and Fernando Hernando and Franciso Montserrat and G.R. Pellikaan",

year = "2018",

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doi = "10.1007/978-3-319-96827-8_23",

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Galindo, C, Hernando, F, Montserrat, F & Pellikaan, GR 2018, The Poincaré polynomial of a linear code. in G-M Greuel, L Narváez Macarro & S Xambó-Descamps (uitgave), Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics: Festschrift for Antonio Campillo on the Occasion of his 65th Birthday. Springer, Cham, blz. 525-535. https://doi.org/10.1007/978-3-319-96827-8_23

The Poincaré polynomial of a linear code. / Galindo, Carlos; Hernando, Fernando ; Montserrat, Franciso et al.
Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics: Festschrift for Antonio Campillo on the Occasion of his 65th Birthday. uitgave / Gert-Martin Greuel; Luis Narváez Macarro; Sebastià Xambó-Descamps. Cham: Springer, 2018. blz. 525-535.

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Hoofdstuk › Academic › peer review

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N2 - 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.

AB - 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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Galindo C, Hernando F, Montserrat F, Pellikaan GR. The Poincaré polynomial of a linear code. In Greuel GM, Narváez Macarro L, Xambó-Descamps S, redacteurs, Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics: Festschrift for Antonio Campillo on the Occasion of his 65th Birthday. Cham: Springer. 2018. blz. 525-535 doi: 10.1007/978-3-319-96827-8_23

The Poincaré polynomial of a linear code

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