Research Output

List of Publications

80 publications  ·  2 granted patents  ·  2 invention disclosures  ·  compiled

Category A1

Refereed Journal Articles

Peer-reviewed original research in scientific journals

  1. 1
    I. Blanco-Chacon, A. F. Boix, M. Greferath, E. Hieta-aho. MacWilliams duality for rank metric codes over finite chain rings. Finite Fields and Their Applications, 103 (2025).
  2. 2
    N. Karimi, A. Y. Darani, and M. Greferath. Correcting adversarial errors with generalized regenerating codes. Advances in Mathematics of Communications (AMC), 18 (2024), 128–140.
  3. 3
    E. Tekin, O. W. Gnilke, F. Ozbudak, B. Blümich, and M. Greferath. Almost perfect autocorrelation sequences with small number of pauses for applications in magnetic resonance. Cryptography and Communications, 16 (2024), 109–127.
  4. 4
    N. Gassner, M. Greferath, J. Rosenthal, and V. Weger. Bounds for Coding Theory over Rings. Entropy 24 (2022), 1473–1489.
  5. 5
    M. V. Dinesen, O. W. Gnilke, M. Greferath, and C. Roessing. Group Testing via Residuation and Partial Geometries. AMC 18 (2024), 9 pages.
  6. 6
    M. Greferath, and C. Roessing. Group Testing with Error-Correction Capabilities for General Pandemics. Elsevier IFAC-PapersOnLine, 55 (2022), 295–298.
  7. 7
    A. Görges, S. Benders, M. Greferath, M. Küppers, M. Adams, and B. Blümich. Selective magnetic resonance signal suppression by colored Frank excitation. Journal of Magnetic Resonance 317 (2020), 10 pages.
  8. 8
    M. Greferath, Y. Lu, M. Shi, P. Sole. Linear Codes over Finite Rings are Trace Codes. Discrete Mathematics 343 (2020), 10 pages.
  9. 9
    M. Greferath, Z. Liu, X. Wu, and J. Zumbrägel. New Results on the Pseudo-Redundancy. Bulletin of the Korean Mathematical Society 56 (2019), 111–130.
  10. 10
    O. Gnilke, M. Greferath, and C. Hollanti, G. Nunez-Ponasso, P. O'Cathain, and E. Swartz. Improved user-private information retrieval via finite geometry. Designs, Codes, and Cryptography 87 (2019), 665–677.
  11. 11
    O. Gnilke, M. Greferath, T. Honold, J. Wood, and J. Zumbrägel. A Characterization of all bi-invariant Weights on a Finite Frobenius Module that allow for the Extension Theorem. Contemporary Mathematics 727 (2019), 117–129.
  12. 12
    O. Gnilke, M. Greferath, and M. Pavcevic. Mosaics of Combinatorial Designs. Designs, Codes, and Cryptography 83 (2018), 13 pages.
  13. 13
    T. Honold, C. McFadden, M. Greferath, J. Wood, J. Zumbrägel. MacWilliams' Extension Theorem for Bi-Invariant Weights over Finite Principal Ideal Rings. Journal of Combinatorial Theory Series A, 125 (2014), 177–193.
  14. 14
    C. Laustsen, M. Greferath, S. Ringaard, N. C. Nielsen, and J. H. Ardenkjaer-Larsen. A new RF tagging pulse based on the Frank poly-phase perfect sequence. Journal of Magnetic Resonance 247 (2014), 50–53.
  15. 15
    C. McFadden, M. Greferath, J. Zumbrägel. Characteristics of invariant weights related to code equivalence over rings. Designs, Codes, and Cryptography 66 (2013), 145–156.
  16. 16
    E. Byrne, M. Greferath, J. Pernas, J. Zumbrägel. Algebraic decoding of negacyclic codes over ℤ₄. Designs, Codes, and Cryptography 66 (2013), 3–16.
  17. 17
    E. Byrne, M. Greferath, A. Kohnert, and V. Skachek. New Bounds for Codes over Finite Frobenius Rings. Designs, Codes and Cryptography 57 (2010), no. 2, 169–179.
  18. 18
    M. F. Flanagan, V. Skachek, E. Byrne, and M. Greferath. Linear-Programming Decoding of Nonbinary Linear Codes. IEEE Transactions on Information Theory 55 (2009), 4134–4154.
  19. 19
    B. Blümich, X. Gong, M. Greferath, and E. Byrne. NMR with Excitation Modulated by Frank Sequences. Journal of Magnetic Resonance 199 (2009), 18–24.
  20. 20
    M. Greferath and R. Therkelsen. On Coloured Constant Composition Multiset Designs. Discrete Mathematics 309 (2009), no. 8, 2410–2416.
  21. 21
    E. Byrne, M. Greferath, and T. Honold. Ring Geometries, Two-Weight Codes, and Strongly Regular Graphs. Designs, Codes and Cryptography 48 (2008), 1–16.
  22. 22
    E. Byrne, M. Greferath, and M. O'Sullivan. The Linear Programming Bound for Codes over finite Frobenius Rings. Designs, Codes and Cryptography 42 (2007), 289–301.
  23. 23
    M. Greferath, G. McGuire, and M. O'Sullivan. On Plotkin-optimal codes over finite Frobenius rings. Journal of Algebra and its Applications 5 (2006), 799–815.
  24. 24
    M. van Dijk, S. Egner, M. Greferath, and A. Wassermann. On two doubly even self-dual binary codes of length 160 and minimum weight 24. IEEE Transactions on Information Theory 51 (2005), 408–411.
  25. 25
    M. Greferath and M. O'Sullivan. On bounds for codes over finite Frobenius rings under the homogeneous weight. Discrete Mathematics 289 (2004), 11–24.
  26. 26
    M. Greferath, A. A. Nechaev, and R. Wisbauer. Finite Quasi-Frobenius Modules and Linear Codes. Journal of Algebra and Applications, 3 (2004), 247–272.
  27. 27
    M. Greferath and C. Rößing. On the Cardinality of Intersection Sets in Inversive Planes. Journal of Combinatorial Theory Series A, 100 (2002), 181–188.
  28. 28
    M. Greferath. Orthogonality Matrices for Modules over Finite Frobenius Rings and MacWilliams' Equivalence Theorem. Finite Fields and Applications 8 (2002), 323–331.
  29. 29
    I. M. Duursma, M. Greferath, S. Litsyn, and S. E. Schmidt. A ℤ₈-linear lift of the binary Golay Code and a non-linear binary (96, 2³⁷, 24)-Code. IEEE Transactions on Information Theory 47 (2001), 1596–1598.
  30. 30
    M. Greferath and S. E. Schmidt. Finite-Ring Combinatorics and MacWilliams's Equivalence Theorem. Journal of Combinatorial Theory Series A 92 (2000), no. 1, 17–28.
  31. 31
    I. M. Duursma, M. Greferath, and S. E. Schmidt. On the Optimal ℤ₄-Codes of Type II and length 16. Journal of Combinatorial Theory Series A 92 (2000), no. 1, 77–82.
  32. 32
    M. Greferath and S. E. Schmidt. Gray Isometries for Finite Chain Rings. IEEE Transactions on Information Theory 45 (1999), 2522–2524.
  33. 33
    M. Greferath and S. E. Schmidt. Linear Codes and Rings of Matrices. Applied Algebra, Algebraic Algorithms and Error Correcting Codes, LNCS 1719, Springer 1999, 160–169.
  34. 34
    M. Greferath and E. Viterbo. On ℤ₄ and ℤ₉-linear Lifts of the Golay Codes. IEEE Transactions on Information Theory 45 (1999), 2524–2527.
  35. 35
    M. Greferath and U. Vellbinger. Efficient Decoding of ℤpk-linear Codes. IEEE Transactions on Information Theory 44 (1998), 1288–1291.
  36. 36
    M. Greferath and U. Vellbinger. On the Extended Error-Correcting Capabilities of the Quaternary Preparata Codes. IEEE Transactions on Information Theory 44 (1998), 2018–2019.
  37. 37
    M. Greferath. Cyclic Codes over Finite Rings. Journal of Discrete Mathematics 177 (1997), 273–277.
  38. 38
    M. Greferath. A Geometric Approach to Free Left Modules over Right Bezout Domains. Geometriae Dedicata 60 (1996), 219–224.
  39. 39
    M. Greferath and S. E. Schmidt. On Stable Geometries. Geometriae Dedicata 51 (1994), 181–199.
  40. 40
    M. Greferath and S. E. Schmidt. On Point-Irreducible Projective Geometries. Journal of Geometry 50 (1994), 73–83.
  41. 41
    P. Blümler, M. Greferath, B. Blümich, and H. W. Spiess. NMR Imaging of Objects Containing Similar Substructures. Journal of Magnetic Resonance A 103 (1993), 142–150.
  42. 42
    M. Greferath, B. Blümich, W. M. Griffith, and G. L. Hoatson. Saturation in Deuteron Hadamard NMR Spectroscopy of Solids. Journal of Magnetic Resonance A 102 (1993), 73–80.
  43. 43
    M. Greferath. Global-Affine Morphisms of Projective Lattice Geometries. Resultate Mathematik 24 (1993), 76–83.
  44. 44
    M. Greferath and S. E. Schmidt. On Barbilian Spaces in Projective Lattice Geometries. Geometriae Dedicata 43 (1992), 337–349.
  45. 45
    M. Greferath and S. E. Schmidt. A Unified Approach to Projective Lattice Geometries. Geometriae Dedicata 43 (1992), 243–264.
  46. 46
    M. Greferath. Zur Hyperebenenalgebraisierung in desarguesschen projektiven Verbandsgeometrien. Journal of Geometry 42 (1991), 100–108.
Category A3

Books & Book Chapters

Edited volumes, chapters in research books, and encyclopedia entries

  1. 47
    M. Greferath, M. O. Pavcevic, N. Silberstein, and M. A. Vazquez-Castro (eds.). Network Coding and Subspace Designs. Signals and Communication Technology, Springer 2018.
  2. 48
    M. Greferath, C. Rößing, and L. Storme. Galois geometries and LDPC codes. In: Current Research Topics in Galois Geometry, Leo Storme and Jan De Beule (eds.), Nova Handbook on Galois Geometries, 2011.
  3. 49
    M. Greferath. An Introduction to Ring-Linear Coding Theory. In: Gröbner Bases, Coding and Cryptography, Max Sala et al. (eds.), Springer Verlag 2009.
  4. 50
    M. Greferath. On Golay Codes. In: G. Proakis (ed.), Wiley Encyclopedia of Telecommunications, 1st edition, 2003, 885–892.
  5. 51
    M. Greferath and S. E. Schmidt. Projective Lattice Geometries. In: G. Grätzer, General Lattice Theory, Birkhäuser, 1998, 539–553.
  6. 52
    U. Brehm, M. Greferath, and S. E. Schmidt. Projective Geometry on Modular Lattices. In: F. Buekenhout, Handbook of Incidence Geometry. North-Holland, Amsterdam 1995, 1115–1142.
Category A4

Conference Proceedings

Peer-reviewed contributions to refereed international conferences

  1. 53
    F. Blomqvist and M. Greferath. The Double-Plane Algorithm: a Simple Algorithm for the Closest Vector Problem. Proc. IEEE International Symposium on Information Theory and its Applications (ISITA 2018).
  2. 54
    Z. Liu, J. Zumbrägel, M. Greferath, X.-W. Wu. Notes on Pseudoredundancy. Proc. IEEE International Symposium on Information Theory (ISIT 2014), Honolulu, HI, USA.
  3. 55
    M. Greferath, J. Zumbrägel. A Grey-Rankin Bound for Codes over Frobenius Rings. Proc. 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), Groningen, The Netherlands.
  4. 56
    E. Byrne, M. Greferath, J. Pernas, J. Zumbrägel. Algebraic decoding of negacyclic codes over ℤ₄. Proc. Seventh International Workshop on Coding and Cryptography (WCC 2011), Paris, France 2011.
  5. 57
    M. Greferath, J. Zumbrägel. On the algebraic representation of selected optimal non-linear binary codes. Proc. IEEE International Symposium on Information Theory (ISIT 2012), Cambridge, MA, USA, pp. 3115–3119.
  6. 58
    C. McFadden, M. Greferath, J. Zumbrägel. Characteristics of invariant weights related to code equivalence over rings. Proc. Seventh International Workshop on Coding and Cryptography (WCC 2011), Paris, France 2011.
  7. 59
    M. Greferath and A. A. Nechaev. Generalized Frobenius Extensions of Finite Rings and Trace Functions. Proceedings of the IEEE Information Theory Workshop, Dublin 2010.
  8. 60
    M. Flanagan, V. Skachek, E. Byrne, and M. Greferath. Linear-programming Decoding of Non-binary Linear Codes. Proceedings of the SCC'08, Ulm 2008.
  9. 61
    V. Skachek, M. F. Flanagan, E. Byrne, and M. Greferath. Polytope representations for linear-programming decoding of non-binary linear codes. IEEE International Symposium on Information Theory (2008), 1508–1512.
  10. 62
    B. Blümich, F. Casanova, E. Danieli, Q. Gong, M. Greferath, A. Haber, J. Kolz, J. Perlo. Moving NMR. AIP Conference Proceedings 1081:3–6.
  11. 63
    M. Flanagan, M. Greferath, and C. Roessing. On LDPC Codes from (0,1)-Geometries induced by Finite Inversive Spaces of Even Order. Proceedings of WCC-2007, Versailles, France (2007).
  12. 64
    M. Greferath and T. Honold. Monomial Extensions of Isometries between Codes over ℤₘ, II: Invariant Weight Functions. Proceedings of the ACCT-10, Zvenigorod, Russia 2006.
  13. 65
    M. Greferath and S. Lopez-Permouth. On the Role of Rings and Modules in Algebraic Coding Theory. Proceedings of the Ubatuba Conference on Groups, Rings and Group Rings, Ubatuba, Brazil 2004.
  14. 66
    M. Greferath and T. Honold. On Weights Allowing for MacWilliams' Equivalence Theorem. Proceedings of the OC-2005, Pamporovo Bulgaria, 2005, 182–189.
  15. 67
    E. Byrne, M. Greferath, and T. Honold. Two-Weight Codes over Finite Frobenius Rings and Strongly Regular Graphs. Proceedings of the OC-2005, Pamporovo Bulgaria, 2005, 64–73.
  16. 68
    M. Greferath and S. E. Schmidt. Multi-Secret Sharing Schemes Based on Finite Geometry over Rings and Modules. In: Recent advances in Geometry and Topology, 187–194, Cluj Univ. Press, Cluj, 2004.
  17. 69
    M. Greferath, M. O'Sullivan, and R. Smarandache. Construction of Good LDPC Codes using Dilation Matrices. Proceedings of the ISIT 2004, Chicago, June 2004.
  18. 70
    M. van Dijk, S. Egner, M. Greferath, and A. Wassermann. On binary linear [160, 80, 24]-codes. Proceedings of the ISIT 2003, Japan, June 2003, 162.
  19. 71
    M. O'Sullivan, M. Greferath, and R. Smarandache. Construction of LDPC Codes from Affine Permutation Matrices. Proceedings of the Allerton Conference 2002, Urbana-Champaign (IL), 2002, 1159–1167.
  20. 72
    M. O'Sullivan, M. Greferath, and R. Smarandache. Analysis of Iterative Decoding Algorithms. Proceedings of 15th International Symposium on the Mathematical Theory of Networks and Systems, Notre Dame, IN, 2002.
  21. 73
    I. M. Duursma, M. Greferath, S. Litsyn, and S. E. Schmidt. A ℤ₉-Linear Code Inducing a Ternary (72, 3²⁵, 24)-Code. Proceedings of the OC'2001, Slantchev Briag, Bulgaria, 2001, 59–64.
  22. 74
    M. Greferath. On Artinian and Noetherian Projective Lattice Geometries. In: Algebra and its Applications (Athens, OH, 1999), Contemporary Mathematics 259, AMS, Providence, RI, 2000, 241–246.
  23. 75
    M. Greferath and S. E. Schmidt. Linear Codes and Rings of Matrices. Proceedings of AAECC 13, Hawaii 1999.
  24. 76
    M. Greferath and E. Viterbo. Algebraic Construction of Good Collision Resistant Signal Sets. Proceedings of the Workshop on Coding and Cryptography (WCC 1999) France, 213–224.
  25. 77
    M. Greferath and S. E. Schmidt. Secret Sharing on Partially Ordered Sets. Proceedings of the ISIT 1998, MIT Boston 1998, p. 299.
Categories B, G & H

Other Publications, Theses & Patents

Preprints, doctoral dissertations, and patents/invention disclosures

Non-refereed Articles

  1. 78
    I. M. Duursma and M. Greferath. Computing Symmetrized Weight Enumerators for Lifted Quadratic Residue Codes. arXiv:math/0302132, 2003.

Theses

  1. 79
    Zur Rolle der Ringe und Moduln in der Algebraischen Codierungstheorie und Kryptologie. Habilitationsschrift. Mitteilungen Math. Sem. Gießen 245 (2001).
  2. 80
    Zur Strukturtheorie der projektiven Verbandsgeometrie. Dissertation. Mitteilungen Math. Sem. Gießen 217 (1994).

Granted Patents

  1. P1
    E. Byrne, M. Greferath, X. Gong, and B. Blümich. Method for performing magnetic resonance measurements and apparatus for executing said method. Patent WO2010043548 A1, US8952691 B2 (2010). ✓ Granted
  2. P2
    O. Gnilke, M. Greferath, F. Ozbudak, and E. Tekin. An infinite family of polyphase sequences with ideal autocorrelation properties allowing for a single PAUSE. ✓ Granted

Invention Disclosures

  1. D1
    M. Flanagan, M. Greferath, and C. Rößing. An encoding scheme and a decoding scheme using a series of LDPC codes based on finite inversive spaces. WO2008/125300 A2 (2008). Published after patent application.
  2. D2
    M. O'Sullivan, M. Greferath, and R. Smarandache. Sparse Matrices with Large Girth. Invention disclosure, San Diego State University 2003.