Natalia Dück

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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)
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)
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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