Group for Discrete Mathematics

(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. 33:3 (2021), p. 499-513, doi: 10.1007/s00498-021-00289-9.

(11) Alfarano, G. N.; Lieb, J.; Rosenthal, J.: Construction of LDPC convolutional codes via difference triangle sets, Designs, Codes and Cryptography 89 (2021), p. 2235-2254.

(12) 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.

(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.

(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 Gröbner 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.

(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.

(1) Lieb, J.; Napp, D.; Pinto, R.: Robust low-delay streaming PIR using convolutional codes, arXiv:1911.01316v2.

(2) Heri, S.; Lieb, J.; Rosenthal, J.: Self-Dual Convolutional Codes, arXiv:2208.04087.

(3) Abreu, Z.; Lieb, J.; Pinto, R.; Rosenthal, J.: Criteria for the construction of MDS convolutional codes with good columndistances, arXiv:2305.04647.

Lieb, J.: Counting Polynomial Matrices over Finite Fields. Matrices with Certain Primeness Properties and Applications to Linear Systems and Coding Theory, Würzburg University Press 2017 (available at: opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/15130).