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.

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Profiles

Jacob R. Appelbaum

j.appelbaum@tue.nl

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

t.ashur@tue.nl

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

Person: UD : Assistant Professor

Nikhil Bansal

n.bansal@tue.nl

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

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 proceeding › Conference contribution › Academic › peer-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 proceeding › Conference contribution › Academic › peer-review

Cryptography

Decoding

Standardization