Julia Lieb

About

I am currently assistant professor in Discrete Mathematics at TU Ilmenau, Germany.

Research Interests

Convolutional Codes, Quasi-cyclic Codes, LDPC Codes, Code-based Cryptography, Linear Systems over Finite Fields, Polynomial Matrices

List of Co-authors

Zita Abreu, Gianira Nicoletta Alfarano, Paulo Almeida, Henry Chimal-Dzul, Niklas Gassner, Anina Gruica, Uwe Helmke, Sebastian Heri, Jens Jordan, Abhinaba Mazumder, Diego Napp, Raquel Pinto, Joachim Rosenthal, Michael Schaller, Simran Tinani, Carlos Vela

Publications

Journal papers

1. Helmke, U.; Jordan, J.; Lieb, J.: Probability estimates for reachability of linear systems defined over finite fields, Advances in Mathematics of Communications 10 No. 1 (2016), p. 63-78.
2. Lieb, J.: The probability of primeness for specially structured polynomial matrices over finite fields with applications to linear systems and convolutional codes, Math. Control Signals Syst. 29:8 (2017), doi:10.1007/s00498-017-0191-z.
3. Lieb, J.: Uniform probability and natural density of mutually left coprime polynomial matrices over finite fields, Lin. Alg. Appl. 539 (2018), p. 134-159.
4. Lieb, J.: Complete MDP convolutional codes, Journal of Algebra and Its Applications 8:6 (2019) 1950105 (13 pages).
5. Lieb, J.: Necessary field size and probability for MDP and complete MDP convolutional codes, Des. Codes Cryptogr. 87:12 (2019), p. 3019-3043.
6. Lieb, J.; Pinto, R.: Constructions of MDS convolutional codes using superregular matrices, J. Algebra Comb. Discrete Appl. 7:1 (2020), p. 71-82.
7. Almeida, P.; Lieb, J.: Complete j-MDP convolutional codes, IEEE Transactions on Information Theory, doi: 10.1109/TIT.2020.3015698, 2020.
8. Alfarano, G. N.; Lieb, J.: On the left primeness of some polynomial matrices with applications to convolutional codes, Journal of Algebra and Its Applications, doi: 10.1142/S0219498821502078, 2020.
9. Lieb, J.; Napp, D.; Pinto, R.: List decoding of Convolutional Codes over integer residue rings, Finite Fields and Their Applications 72 (2021), 101815.
10. Lieb, J.; Rosenthal, J.: Erasure decoding of convolutional codes using first-order representations, Math. Control Signals Syst., https://doi.org/10.1007/s00498-021-00289-9, 2021.
11. Lieb, J.; Pinto, R.: A decoding algorithm for 2D convolutional codes over the erasure channel, Advances in Mathematics of Communications, doi.org/10.3934/amc.2021031, 2021.
12. Alfarano, G. N.; Lieb, J.; Rosenthal, J.: Construction of LDPC convolutional codes via difference triangle sets, Designs, Codes and Cryptography, doi.org/10.1007/s10623-021-00912-5, 2021.
13. Alfarano, G. N.; Gruica, A.; Lieb, J.; Rosenthal, J.: Convolutional codes over finite chain rings, MDP codes and their characterization, Advances in Mathematics of Communications, doi: 10.3934/amc.2022028, 2022.
14. Heri, S.; Lieb, J.; Rosenthal, J.: Self-Dual Convolutional Codes, IEEE Transactions on Information Theory 70:2 (2024), p. 950-963, doi: 10.1109/TIT.2023.3343108.
15. Abreu, Z.; Lieb, J.; Pinto, R.; Rosenthal, J.: Criteria for the construction of MDS convolutional codes with good column distances, Advances of Mathematics in Communications 18:2 (2024), p. 595-613, doi: 10.3934/amc.2023060.
16. Lieb, J., Pinto, R., Vela, C.: A new method for erasure decoding of convolutional codes, Designs, Codes & Cryptography (2025), https://doi.org/10.1007/s10623-025-01623-x.
17. Gassner, N.; Lieb, J.; Mazumder, A.; Schaller, M.: Information-Set Decoding for Convolutional Codes, Designs, Codes & Cryptography (2025), doi: 10.1007/s10623-025-01649-1.

Chapters of books

1. Lieb, J.; Pinto, R.; Rosenthal, J.: Convolutional Codes, in "Concise Encyclopedia of Coding Theory" (eds. Huffman, C; Kim, J.; Sole, P.), CRC Press, 2021.

Conference proceedings

1. Helmke, U.; Jordan, J.; Lieb, J.: Reachability of random linear systems over finite fields, in Coding Theory and Applications, 4th International castle Meeting, Palmela Castle, Portugal (eds. Pinto, R.; Malonek, P.R.; Vettori, P.), Springer- Verlag (2014), p. 217-225.
2. Alfarano, G. N.; Lieb, J.; Rosenthal, J.: Construction of rate (n-1)/n non-binary LDPC convolutional codes via difference triangle sets, IEEE International Symposium on Information Theory (ISIT), 2020.
3. Lieb, J.; Tinani, S.: A Number Theoretic Approach to Cycles in LDPC Codes, IFAC-PapersOnLine, Volume 55, Issue 30, 2022, Pages 67-72, doi:10.1016/j.ifacol.2022.11.030.
4. Chimal-Dzul, H.; Lieb, J.; Rosenthal, J.: Generator Matrices of Quasi-cyclic Codes over Extension Fields Obtained from Gr\"obner Basis, IFAC-PapersOnLine, Volume 55, Issue 30, 2022, Pages 61-66, doi:10.1016/j.ifacol.2022.11.029.
5. Abreu, Z.; Lieb, J.; Rosenthal, J.: Binary convolutional codes with optimal column distances, IEEE International Symposium on Information Theory (ISIT), 2023.
6. Abreu, Z.; Lieb, J.; Schaller, M.: An improved Viterbi algorithm for a class of optimal binary convolutional codes, IEEE International Symposium on Information Theory (ISIT), 2024.

Dissertation

• Lieb, J.: Polynomial Matrices over Finite Fields. Matrices with Certain Primeness Properties and Applications to Linear Systems and Coding Theory, Würzburg University Press, 2017.

Talks

Invited talks

1. Probability Estimations for Networks of Linear Systems and their Correlation with Interconnected Convolutional Codes, University of Zurich (04/2016)
2. Probability estimates for networks of linear systems and convolutional codes, University of Aveiro/Portugal (03/2017)
3. Construction of MDP convolutional codes, University of Neuenburg/Switzerland (10/2017)
4. Construction of MDP convolutional codes, TU Munich (01/2018)
5. MDP Faltungscodes, University of Konstanz/Germany (02/2018)
6. The Connection between Discrete-Time Linear systems and Convolutional Codes, University of Würzburg/Germany (01/2019)
7. The problem of constructing complete MDP convolutional codes over small fields, University of Alicante/Spain (06/2019)
8. Convolutional codes, University of Passau/Germany (05/2021)
9. Data Transmission with Convolutional codes, University of Bern (03/2022)
10. Data transmission with convolutional codes, TU Kaiserslautern/Germany (10/2022)
11. The relationship between non-catastrophicity and other properties of convolutional codes, University of Aveiro/Portugal (11/2022)
12. The relationship between non-catastrophicity and other properties of convolutional codes, University of Alicante/Spain (02/2023)
13. Self-dual convolutional codes, University of Aveiro/Portugal (03/2024)
14. On a class of convolutional codes with optimal column distances and efficient decoding algorithm, University of Zurich (09/2024)

Talks on conferences

1. Reachability of Random Linear Systems over Finite Fields, Fourth International Castle Meeting on Coding Theory and Applications (4ICTMA) at Castle of Palmela/Portugal (09/2014)
2. Probability of Reachability for networks of linear Systems over Finite Fields, 7th Workshop on Coding and Systems, Salamanca/Spain (06/2015)
3. Probability Estimations for Linear Systems and Convolutional Codes, Dagstuhl Seminar ”Coding Theory in the Time of Big Data” (08/2016)
4. Probability estimates for networks of linear systems over finite fields and Applications to convolutional codes, Workshop on Networks of Linear Systems and Operator Theory, Sde Boker, Israel (03/2017)
5. The problem of constructing (complete) MDP convolutional codes over small fields, Dagstuhl Seminar ”Algebraic Coding Theory for Networks, Storage, and Security“ (12/2018)
6. MDP convolutional codes, SIAM Conference on Applied Algebraic Geometry, Bern (07/2019)
7. Construction of LDPC convolutional codes, National Meeting of the Portuguese Society for Mathematics (ENSPM), online (07/2021)
8. Erasure decoding of convolutional codes with the help of linear systems, Coding theory and cryptography, A conference in honor of Joachim Rosenthal's 60th birthday, Zurich (07/2022)
9. Self-dual convolutional codes, VI Congreso de Jóvenes Investigadores de la Real Sociedad Matemática Española, Leon, Spain (02/2023)
10. A novel criterion for the construction of MDS convolutional codes of rate 1/n, ALgebraic and combinatorial methods for COding and CRYPTography (ALCOCRYPT), CIRM, Marseille (02/2023)
11. Criteria for the construction of MDS convolutional codes with good column distances, Workshop on Convolutional Codes, Zurich (06/2023)
12. On the Algebraic Structure of Quasi-cyclic Codes and Galois Invariance, SIAM Conference on Applied Algebraic Geometry (AG23), Eindhoven, Netherlands (07/2023)
13. Zusammenhänge zwischen linearen Systemen über endlichen Körpern und Faltungscodes, 16. Elgersburg Workshop Mathematische Systemtheorie, Ilmenau (02/2024)
14. Matrix completion with convolutional codes, Coding Theory and Cryptography, Summer School and Collaboration Workshop, Riva San Vitale, Switzerland (07/2024)
15. An improved Viterbi algorithm for a class of optimal binary convolutional codes, International Symposium on Information Theory (ISIT 2024), Athens (07/2024)
16. Construction of codes over fields of characteristic 2 for easy repair in distributed storage systems, Error-Correcting codes and Combinatorial Structures Workshop, Eindhoven, Netherlands (03/2025)

Seminar talks in own working group

1. Teilerfremde Polynome über endlichen Körpern, University of Würzburg/Germany (06/2014)
2. Probability Estimations for Networks of Linear Systems and their Relationship to Interconnected Convolutional Codes, University of Zurich (12/2016)
3. Anzahlberechnungen für lineare Systeme über endlichen Körpern und Faltungscodes, University of Würzburg/Germany (06/2017)
4. Construction of MDP Convolutional Codes, University of Würzburg/Germany (11/2017)
5. The problem of constructing complete MDP convolutional codes over small fields, University of Aveiro/Portugal (07/2019)

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