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- Natalia Dück, Karl-Heinz Zimmermann
- ArXiv
- 2014

Linear codes over any finite field can be associated to binomial ideals. Focussing on two specific instances, called the code ideal and the generalized code ideal, we present how these binomial ideals can be computed from toric ideals by substituting some variables. Drawing on this result we further show how their Graver bases as well as their universal… (More)

- Natalia Dück, Karl-Heinz Zimmermann
- ArXiv
- 2014

Recently, it was shown that a binary linear code can be associated to a binomial ideal given as the sum of a toric ideal and a non-prime ideal. Since then two different generalizations have been provided which coincide for the binary case. In this paper, we establish some connections between the two approaches. In particular, we show that the corresponding… (More)

- Natalia Dück, Irene Márquez-Corbella, Edgar Martínez-Moro
- ICMCTA
- 2014

We will show how one can compute all reduced Gröbner bases with respect to a degree compatible ordering for code ideals even though these binomial ideals are not toric. To this end, the correspondence of linear codes and binomial ideals will be briefly described as well as their resemblance to toric ideals. Finally, we will hint at applications of the… (More)

- Natalia Dück, Karl-Heinz Zimmermann
- ArXiv
- 2013

Gröbner bases can be used for computing the Hilbert basis of a numerical submonoid. By using these techniques, we provide an algorithm that calculates a basis of a subspace of a finite-dimensional vector space over a finite prime field given as a matrix kernel. AMS Subject Classification: 13P10, 94B05

- Natalia Dück, Karl-Heinz Zimmermann
- Des. Codes Cryptography
- 2015

- Natalia Dück, Irene Marquez Corbella, Edgar Martínez-Moro
- ACM Comm. Computer Algebra
- 2015

The Gröbner fan of an ideal in the commutative polynomial ring consists of polyhedral cones indexing the different leading ideals and is thus the geometric collection of all reduced Gröbner bases for this ideal. One application of the Gröbner fan is the so-called Gröbner walk which is the conversion of Gröbner bases. With the software system TiGERS (Toric… (More)

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