On dual toric complete intersection codes

Pinar Celebi Demirarslan; Ivan Soprunov

doi:10.1016/j.ffa.2014.12.001

On dual toric complete intersection codes

Pinar Celebi Demirarslan
, Ivan Soprunov

Bartin University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper we study duality for evaluation codes on intersections of ℓ hypersurfaces with given ℓ-dimensional Newton polytopes, so called toric complete intersection codes. In particular, we give a condition for such a code to be quasi-self-dual. In the case of ℓ=2 it reduces to a combinatorial condition on the Newton polygons. This allows us to give an explicit construction of dual and quasi-self-dual toric complete intersection codes. We provide a list of examples over F16 and an algorithm for producing them.

Original language	English
Pages (from-to)	118-136
Number of pages	19
Journal	Finite Fields and their Applications
Volume	33
DOIs	https://doi.org/10.1016/j.ffa.2014.12.001
State	Published - Jan 1 2015

Keywords

Ehrhart polynomial
Evaluation code
Lattice polytope
Sparse polynomial system

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10.1016/j.ffa.2014.12.001

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abstract = "In this paper we study duality for evaluation codes on intersections of ℓ hypersurfaces with given ℓ-dimensional Newton polytopes, so called toric complete intersection codes. In particular, we give a condition for such a code to be quasi-self-dual. In the case of ℓ=2 it reduces to a combinatorial condition on the Newton polygons. This allows us to give an explicit construction of dual and quasi-self-dual toric complete intersection codes. We provide a list of examples over F16 and an algorithm for producing them.",

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AU - Soprunov, Ivan

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N2 - In this paper we study duality for evaluation codes on intersections of ℓ hypersurfaces with given ℓ-dimensional Newton polytopes, so called toric complete intersection codes. In particular, we give a condition for such a code to be quasi-self-dual. In the case of ℓ=2 it reduces to a combinatorial condition on the Newton polygons. This allows us to give an explicit construction of dual and quasi-self-dual toric complete intersection codes. We provide a list of examples over F16 and an algorithm for producing them.

AB - In this paper we study duality for evaluation codes on intersections of ℓ hypersurfaces with given ℓ-dimensional Newton polytopes, so called toric complete intersection codes. In particular, we give a condition for such a code to be quasi-self-dual. In the case of ℓ=2 it reduces to a combinatorial condition on the Newton polygons. This allows us to give an explicit construction of dual and quasi-self-dual toric complete intersection codes. We provide a list of examples over F16 and an algorithm for producing them.

KW - Ehrhart polynomial

KW - Evaluation code

KW - Lattice polytope

KW - Sparse polynomial system

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VL - 33

SP - 118

EP - 136

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

ER -

On dual toric complete intersection codes

Abstract

Keywords

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