• Postbus 513, MF

    5600MB Eindhoven

    Netherlands

Organization profile

Introduction / mission

The three chairs within DM maintain the three main research areas: the more applied coding theory and cryptology; the combinatorial optimization which goes into problems in operational management; and the more fundamental discrete algebra and geometry.

Highlighted phrase

The section DM is interested in all mathematical problems of a discrete nature. 

Organisational profile

The section DM has three chairs:

The chair for Coding Theory and Cryptology (CC) performs research in theoretical and applied areas of both topics:

Coding Theory is the mathematical theory of encoding information in such a way that it becomes resistant to transmission errors. The main topics are the study of the properties of various codes (cyclic codes, BCH-codes, MDS-codes, algebraic-geometric codes) and the construction of efficient decoding algorithms for these codes.

Cryptology is the mathematical theory of protecting information against unauthorized access (privacy), determining if a message has been altered by a third party (integrity), adding a signature to an electronic document and verifying the identity.

The Combinatorial Optimization (CO) group focuses on the analysis and solution of discrete algorithmic problems that are computationally difficult (NP-hard). A generic formulation of such problems is: given a number of boundary conditions and constraints, find a solution that minimizes the cost or maximizes the profit.

Phenomena throughout mathematics and the natural sciences have discrete algebraic aspects, often along with analytical counterparts. While the latter are typically modelled using real numbers, differential equations, and numerical computations, describing the discrete-algebraic aspects involves objects like nite elds, graphs, polynomials, groups, algebras, and symbolic computations. The Discrete Algebra and Geometry (DAG) group at the TU/e develops the mathematics needed for such a description.

Network Recent external collaboration on country level. Dive into details by clicking on the dots.

Research Output 1970 2019

An algorithm for komlós conjecture matching Banaszczyk's bound

Bansal, N., Dadush, D. & Garg, S., 30 Apr 2019, In : SIAM Journal on Computing. 48, 2, p. 534-553 20 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Coloring
Colouring
Discrepancy
Set Systems
Efficient Algorithms

Application of complementary dual AG codes to entanglement-assisted quantum codes

Fernandes Pereira, F., Pellikaan, R., Gadioli La Guardia, G. & de Assis, F. M., 2019, (Accepted/In press) Proceedings of the IEEE International Symposium on Information Theory. Piscataway: Institute of Electrical and Electronics Engineers

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

A reaction attack against cryptosystems based on LRPC codes

Samardjiska, S., Santini, P., Persichetti, E. & Banegas, G., 2019, Progress in Cryptology -- LATINCRYPT 2019. Schwabe, P. & Thériault, N. (eds.). Cham: Springer International Publishing Switzerland, p. 197-216 20 p. (Lecture Notes in Computer Science; vol. 11774)

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Cryptography
Decoding
Standardization

Prizes

Algorithms for coping with uncertainty and intractability

Nikhil Bansal (Recipient), 2013

Recognition: ERCConsolidatorScientific

Combinatorial optimization
Approximation algorithms
Computer science
Uncertainty
Optimum design

Best investigative reporting

Jacob Appelbaum (Recipient), 2014

Recognition: OtherCareer, activity or publication related prizes (lifetime, best paper, poster etc.)Scientific

Best Paper Award at IH&MMSec 2015

Thijs Laarhoven (Recipient), 19 Jun 2015

Recognition: OtherCareer, activity or publication related prizes (lifetime, best paper, poster etc.)Scientific

File

Activities 2014 2019

  • 15 Contributed talk
  • 6 Invited talk
  • 1 Workshop, seminar, course or exhibition

Entanglement-assisted Quantum Error Correcting Codes from Algebraic Geometry Codes

Francisco Fernandes Pereira (Speaker)
30 Nov 2019

Activity: Talk or presentation typesContributed talkScientific

Strong IP Formulations Need Large Coefficients

Christopher Hojny (Speaker)
6 Sep 2019

Activity: Talk or presentation typesContributed talkScientific

Entanglement-Assisted Quantum AG Codes

Francisco Fernandes Pereira (Speaker)
17 Jul 2019

Activity: Talk or presentation typesInvited talkScientific

Student theses

A characterization of the special linear and unitary Lie algebra via its extremal geometry

Author: Oostendorp, M., 31 Aug 2018

Supervisor: Cuypers, F. (Supervisor 1)

Student thesis: Master

File

Achieving differential privacy in secure multiparty computation

Author: Thissen, K., 15 May 2019

Supervisor: Schoenmakers, B. (Supervisor 1), Koster, R. (. (External person) (External coach) & van Liesdonk, P. (External coach)

Student thesis: Master

File

An adaption of the crossbred algorithm for solving multivariate quadratic systems over F2 on GPUs

Author: Ning, K., 27 Nov 2017

Supervisor: Lange, T. (Supervisor 1), Bernstein, D. (External coach) & Niederhagen, R. (External coach)

Student thesis: Master

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