Marcus Greferath - Publications

• M. Greferath: Zur Hyperebenenalgebraisierung in desarguesschen projektiven Verbandsgeometrien. J. Geom. 42 (1991), 100-108.
• M. Greferath, S. E. Schmidt: A Unified Approach to Projective Lattice Geometries. Geom. Dedicata 43 (1992), 243-264.
• M. Greferath, S. E. Schmidt: On Barbilian Spaces in Projective Lattice Geometries. Geom. Dedicata 43 (1992), 337-349.
• M. Greferath: Global-Affine Morphisms of Projective Lattice Geometries. Resultate Math. 24 (1993), 76-83.
• M. Greferath, B. Bluemich, W. M. Griffith, G. L. Hoatson: Saturation in Deuteron Hadamard NMR Spectroscopy of Solids. J. Magn. Reson. A 101 (1993), 73-80.
• P. Bluemler, M. Greferath, B. Bluemich, H. W. Spiess: NMR Imaging of Objects Containing Similar Substructures. J. Magn. Reson. A 103 (1993), 142-150.
• M. Greferath, S. E. Schmidt: On Point-Irreducible Projective Geometries. J. Geometry 50 (1994), 73-83.
• M. Greferath, S. E. Schmidt: On Stable Geometries. Geom. Dedicata 51 (1994), 181-199.
• M. Greferath: A Geometrical Approach to Free Left Modules over Right Bezout Domains. Geom. Dedicata 60 (1996), 219-224.
• M. Greferath: Cyclic Codes over Finite Rings. J. Discr. Math. 177 (1997), 273-277.
• M. Greferath, U. Vellbinger: Efficient Decoding of Z_p^k-linear Codes. IEEE Tran. Inform. Theory 44 (1998), 1288-1291.
• M. Greferath, U. Vellbinger: On the Extended Error-Correcting Capabilities of the Quaternary Preparata Codes. IEEE Trans. Inform. Theory 44 (1998), 2018-2019.
• M. Greferath, E. Viterbo: On Z₄ and Z₉-linear Lifts of the Golay Codes, IEEE Trans. Inform. Theory 45 (1999), 2524-2527.
• M. Greferath, S. E. Schmidt: Linear Codes and Rings of Matrices. Applied Algebra, Algebraic Algorithms and Error Correcting Codes, LNCS 1719, Springer 1999, 160-169.
• M. Greferath, S. E. Schmidt: Gray Isometries for Finite Chain Rings. IEEE Trans. Inform. Theory 45 (1999), 2522-2524.
• M. Greferath, S. E. Schmidt: Finite-Ring Combinatorics and MacWilliams's Equivalence Theorem. J. Combin. Theory Ser. A 92 (2000), no. 1, 17-28.
• I. M. Duursma, M. Greferath, S. E. Schmidt: On the Optimal Z₄-Codes of Type II and length 16. J. Combin. Theory Ser. A 92 (2000), no. 1, 77-82.
• I. M. Duursma, M. Greferath, S. Litsyn, S. E. Schmidt: A Z₈-linear lift of the binary Golay Code and a non-linear binary (96,237,24)-Code. IEEE Trans. Inform. Theory 47 (2001), 1596-1598.
• M. Greferath: Orthogonality Matrices for Modules over Finite Frobenius Rings and MacWilliams' Equivalence Theorem. Finite Fields Appl. 8 (2002), no. 3, 323-331.
• M. Greferath, C. Roessing: On the Cardinality of Intersection Sets in Inversive Planes. J. Comb. Theory Ser. A 100 (2002), 181-188.
• M. Greferath, A. A. Nechaev, R. Wisbauer: Finite Quasi-Frobenius Modules and Linear Codes. J. Algebra Appl. 3 (2004), 247-272.
• M. van Dijk, S. Egner, M. Greferath, A. Wassermann: On two doubly even self-dual binary codes of length 160 and minimum weight 24. IEEE Trans. Inform. Theory 51 (2005), 408-411.
• M. Greferath, M. O'Sullivan: On bounds for codes over finite Frobenius rings under the homogeneous weight. Disc. Mathematics 289 (2005), 11-24.

• U. Brehm, M. Greferath, S. E. Schmidt: Projective Geometry on Modular Lattices. In: F. Buekenhout, Handbook of Incidence Geometry. North-Holland, Amsterdam 1995, 1115-1142.
• M. Greferath: Zur Strukturtheorie der projektiven Verbandsgeometrie. Dissertation. Mitt. Math. Sem. Giessen 217 (1994).
• M. Greferath, S. E. Schmidt: Projective Lattice Geometries. In: G. Graetzer, General Lattice Theory, Birkhaeuser 1998.
• M. Greferath: Zur Rolle der Ringe und Moduln in der Algebraischen Codierungstheorie und Kryptologie. Habilitationsschrift. Mitt. Math. Sem. Giessen 245 (2001).
• M. Greferath: Golay Codes. In: J. Proakis, The Wiley Encyclopedia of Telecommunications, Wiley, January 2003, pp. 885-892.

• M. Greferath, S. E. Schmidt: Secret Sharing on Partially Ordered Sets. Proc. IEEE International Symposium on Information Theory (ISIT 1998), MIT, Boston, USA, p. 299.
• M. Greferath, E. Viterbo: Algebraic Construction of Good Collision Resistent Signal Sets. Proc. Workshop on Coding and Cryptography (WCC 1999), Paris, France, 213-224.
• M. Greferath, S. E. Schmidt: Linear Codes and Rings of Matrices. Proc. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 13), 1999, Hawaii, USA.
• M. Greferath: On Artinian and Noetherian Projective Lattice Geometries. Proc. Algebra and its Applications (Athens, OH, 1999), 241-246, Contemp. Math. 259, Amer. Math. Soc., Providence, RI, 2000.
• I. M. Duursma, M. Greferath, S. Litsyn, S. E. Schmidt: A Z₉-Linear Code Inducing a Ternary (72,325,24)-Code. Proc. Optimal Codes and Related Topics (OC 2001), Slantchev Briag, Bulgaria.
• M. O'Sullivan, M. Greferath, R. Smarandache: Analysis of Iterative Decoding Algorithms. Proc. 15th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2002), Notre Dame, IN, USA.
• M. O'Sullivan, M. Greferath, R. Smarandache: Construction of LDPC Codes from Affine Permutation Matrices. Proc. Allerton Conference 2002, Urbana-Champaign, IL, USA, 1159-1167.
• M. van Dijk, S. Egner, M. Greferath, A. Wassermann: On Binary [160,80,24]-codes. Proc. IEEE International Symposium on Information Theory (ISIT 2003), Yokohama, Japan.
• M. Greferath, M. O'Sullivan, R. Smarandache: Construction of Good LDPC Codes using Dilation Matrices. Proc. International Symposium on Information Theory (ISIT 2004), Chicago, USA.
• M. Greferath, S. E. Schmidt: Multi-Secret Sharing Schemes Based on Finite Geometry over Rings and Modules. Proc. 6th International Workshop on Differential Geometry and Topology and 3rd German-Romanian Seminar on Geometry, 2003, Cluj-Napoca, Romania, 187-194.
• M. Greferath, S. Lopez-Permouth: On the Role of Rings and Modules in Algebraic Coding Theory. Proc. Ubatuba Conference on Groups, Rings and Group Rings, 2004, Ubatuba, Brazil.
• E. Byrne, M. Greferath, T. Honold: Two-Weight Codes over Finite Frobenius Rings and Strongly Regular Graphs. Proc. Optimal Codes and Related Topics (OC 2005), Pamporovo, Bulgaria, 64-70.
• M. Greferath, T. Honold: On Weights Allowing for MacWilliams' Equivalence Theorem. Proc. Optimal Codes and Related Topics (OC 2005), Pamporovo, Bulgaria, 182-189.

• M. Greferath, R. K. Therkelsen: On Coloured Constant Composition Designs. Preprint 2005.
• I. M. Duursma, M. Greferath: Computing Symmetrized Weight Enumerators for Lifted Quadratic Residue Codes. Preprint 2003.
• M. Greferath, G. McGuire, M. E. O'Sullivan: On Plotkin-Optimal Codes over Finite Frobenius Rings. Preprint 2005.
• M. Greferath, T. Honold: Monomial Extensions of Isometries between Codes over Z_m, II: Invariant Weight Functions. Preprint 2005.
• E. Byrne, M. Greferath, T. Honold: Ring Geometries, Two-Weight Codes and Strongly Regular Graphs. Preprint 2005.
• E. Byrne, M. Greferath, M. E. O'Sullivan: The Linear Programming Bound for Codes over Finite Frobenius Rings. Preprint 2005.