Research Output per year

# 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.

## Fingerprint Dive into the research topics where Discrete Mathematics W&I is active. These topic labels come from the works of this organisation's members. Together they form a unique fingerprint.

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

## Profiles

## Jacob R. Appelbaum

- Department of Mathematics and Computer Science, Discrete Mathematics - Doctoral Candidate
- Department of Mathematics and Computer Science, Discrete Mathematics W&I - Doctoral Candidate

Person: Prom. : doctoral candidate (PhD)

## Tomer Ashur

- Department of Mathematics and Computer Science, Discrete Mathematics - Assistant Professor

Person: UD : Assistant Professor

## Nikhil Bansal

- Department of Mathematics and Computer Science, Combinatorial Optimization
- Department of Mathematics and Computer Science, Discrete Mathematics W&I - Full Professor
- Department of Mathematics and Computer Science, Discrete Mathematics - Full Professor

Person: HGL : Professor

## 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 journal › Article › Academic › peer-review

## A new class of irreducible pentanomials for polynomial-based multipliers in binary fields

Banegas, G., Custódio, R. & Panario, D., 1 Nov 2019, In : Journal of Cryptographic Engineering. 9, 4, p. 359–373 15 p.Research output: Contribution to journal › Article › Academic › peer-review

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

Pereira, F. R. F., Pellikaan, R., La Guardia, G. G. & De Assis, F. M., 1 Jul 2019,*2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings.*Piscataway: Institute of Electrical and Electronics Engineers, p. 2559-2563 5 p. 8849685

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

## Prizes

## Algorithms for coping with uncertainty and intractability

N. Bansal (Recipient), 2013

Prize: ERC › Consolidator › Scientific

## Best investigative reporting

Jacob Appelbaum (Recipient), 2014

Prize: Other › Career, activity or publication related prizes (lifetime, best paper, poster etc.) › Scientific

## Best Paper Award at IH&MMSec 2015

Thijs Laarhoven (Recipient), 19 Jun 2015

Prize: Other › Career, activity or publication related prizes (lifetime, best paper, poster etc.) › Scientific

## Activities 2014 2019

## Entanglement-assisted Quantum Error Correcting Codes from Algebraic Geometry Codes

Francisco Fernandes Pereira (Speaker)Activity: Talk or presentation types › Contributed talk › Scientific

## Strong IP Formulations Need Large Coefficients

Christopher Hojny (Speaker)Activity: Talk or presentation types › Contributed talk › Scientific

## Entanglement-Assisted Quantum AG Codes

Francisco Fernandes Pereira (Speaker)Activity: Talk or presentation types › Invited talk › Scientific

## Press / Media

## Fast, Furious and Insecure: Passive Keyless Entry and Start in Modern Supercars

10/09/18 → 27/08/19

2 items of Media coverage

Press/Media: Research

## EECS Distinguished Speaker: Prof. Nikhil Bansal, Professor, Department of Mathematics and Computer Science Eindhoven University of Technology, "Can we Design Clean Algorithms for Messy Problems"

23/10/18

1 item of Media coverage

Press/Media: Expert Comment

## Post-Quanten-Kryptographie — Wenn Ihre Daten auch in Zukunft Geheimnisse bleiben sollen

7/09/18

1 Media contribution

Press/Media: Expert Comment

## Student theses

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

Author: Oostendorp, M., 31 Aug 2018Supervisor: Cuypers, F. (Supervisor 1)

Student thesis: Master

## Achieving differential privacy in secure multiparty computation

Author: Thissen, K., 15 May 2019Supervisor: Schoenmakers, B. (Supervisor 1), Koster, R. (. (External person) (External coach) & van Liesdonk, P. (External coach)

Student thesis: Master

## A group-theoretical analysis of solvability, solutions and solution strategies of permutation puzzles

Author: Rijpert, D. T., 15 Aug 2019Supervisor: Cuypers, H. (Supervisor 1)

Student thesis: Bachelor