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09/07/2023
The complexity of solving a random polynomial system
A multivariate cryptograpic instance in practice is a multivariate polyn...
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07/13/2023
Integer sequences that are generalized weights of a linear code
Which integer sequences are sequences of generalized weights of a linear...
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04/26/2023
MacWilliams' Extension Theorem for rank-metric codes
The MacWilliams' Extension Theorem is a classical result by Florence Jes...
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04/24/2023
Sum-rank metric codes
Sum-rank metric codes are a natural extension of both linear block codes...
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12/23/2022
Generalized column distances
We define a notion of r-generalized column distances for the j-truncatio...
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07/25/2022
Generalized weights of convolutional codes
In 1997 Rosenthal and York defined generalized Hamming weights for convo...
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01/19/2022
Quasi optimal anticodes: structure and invariants
It is well-known that the dimension of optimal anticodes in the rank-met...
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01/15/2022
Generalized weights of codes over rings and invariants of monomial ideals
We develop an algebraic theory of supports for R-linear codes of fixed l...
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12/20/2021
The complexity of solving Weil restriction systems
The solving degree of a system of multivariate polynomial equations prov...
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12/10/2021
Solving degree, last fall degree, and related invariants
In this paper we study and relate several invariants connected to the so...
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07/28/2021
Optimal anticodes, MSRD codes, and generalized weights in the sum-rank metric
Sum-rank metric codes have recently attracted the attention of many rese...
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11/02/2020
Stronger bounds on the cost of computing Groebner bases for HFE systems
We give upper bounds for the solving degree and the last fall degree of ...
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05/06/2019
The complexity of MinRank
In this note, we leverage some of our results from arXiv:1706.06319 to p...
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02/07/2019
Rank-metric codes
This is a chapter of the upcoming "A Concise Encyclopedia of Coding Theo...
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03/28/2018