Dr. Michael Kiermaier

Foto

Address

Lehrstuhl Mathematik II
Universität Bayreuth
95447 Bayreuth
Germany

Phone: +49 (0) 921/55-3382
Fax: +49 (0) 921/55-3385
email: mNicOhael.kiermSaier@uPni-Abayreuth.dMe (remove the six capital letters NOSPAM)
Room number: 3.2.02.736 (building NW II)

My author profiles on MathSciNet, Zentralblatt Math and DBLP.

Publications

  1. Classification of maximal arcs in small projective Hjelmslev Geometries.
    (with Thomas Honold)
    In Proceedings of the Tenth International Workshop on Algebraic and Combinatorial Coding Theory 2006, pages 112–117, 2006.
    arXiv: 1503.02937
  2. New arcs in projective Hjelmslev planes over Galois Rings.
    (with Axel Kohnert)
    In Proceedings of the Fifth International Workshop on Optimal Codes and Related Topics 2007, pages 112–119, 2007.
    arXiv: 1503.02932
  3. Double and bordered α-circulant codes over finite commutative chain rings.
    (with Alfred Wassermann)
    In Proceedings of the Eleventh International Workshop on Algebraic and Combinatorial Coding Theory 2008, pages 144–150, 2008.
    pdf-file on conference homepage
    arXiv: 1503.02939
  4. On the minimum Lee distance of quadratic residue codes over ℤ4.
    (with Alfred Wassermann)
    In Proceedings of the International Symposium on Information Theory (ISIT), pages 2617–2619, 2008.
    Digital Object Identifier: 10.1109/ISIT.2008.4595465
  5. New complete 2-arcs in the uniform projective Hjelmslev planes over chain rings of order 25.
    (with Matthias Koch)
    In Proceedings of the Sixth International Workshop on Optimal Codes and Related Topics 2009, pages 106–113, 2009. pdf-file on conference homepage
    arXiv: 1503.02941
  6. Maximal integral point sets in affine planes over finite fields
    (with Sascha Kurz)
    Discrete Mathematics 309, 13 (2009-7-6), 4564–4575.
    Digital Object Identifier: 10.1016/j.disc.2009.02.020
    arXiv: 1401.2825, 0804.1285
    Mathematical Reviews: MR2519195
    Zentralblatt Math: 1184.51009
  7. New binary singly even self-dual codes
    (with Masaaki Harada, Alfred Wassermann and Radinka Yorgova)
    IEEE Transactions on Information Theory 56, 4 (2010-4), 1612–1617.
    Digital Object Identifier: 10.1109/TIT.2010.2040967
    Mathematical Reviews: MR2648796
  8. New arcs of maximal size in projective Hjelmslev planes of order 9
    (with Thomas Honold and Ivan Landjev)
    Comptes rendus de l’Académie Bulgare des Sciences 63, 2 (2010), 171–180.
    Journal link (pdf available)
    Mathematical Reviews: MR2656196
    Zentralblatt Math: 1224.05503
  9. A new series of ℤ4-linear codes of high minimum Lee distance derived from the Kerdock codes
    (with Johannes Zwanzger)
    In Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems, ISBN 9789633113707, pages 929–932, 2010.
  10. New ring-linear codes from geometric dualization
    (with Johannes Zwanzger)
    In Proceedings of the Seventh International Workshop on Coding and Cryptography, pages 111–120, 2011.
    online version (pdf available)
  11. A ℤ4-linear code of high minimum Lee distance derived from a hyperoval
    (with Johannes Zwanzger)
    Advances in Mathematics of Communications 5, 2 (2011-5), 275–286.
    Digital Object Identifier: 10.3934/amc.2011.5.275
    Mathematical Reviews: MR2801593
    Zentralblatt Math: 1252.94120
  12. 2-arcs of maximal size in the affine and the projective Hjelmslev plane over ℤ25
    (with Matthias Koch and Sascha Kurz)
    Advances in Mathematics of Communications 5, 2 (2011-5), 287–301.
    Digital Object Identifier: 10.3934/amc.2011.5.287
    arXiv: 1401.4340
    Mathematical Reviews: MR2801594
    Zentralblatt Math: 1228.51006
  13. The maximal size of 6- and 7-arcs in projective Hjelmslev planes over chain rings of order 9
    (with Thomas Honold)
    Science China. Mathematics 55, 1 (2012-1), 73–92.
    Digital Object Identifier: 10.1007/s11425-011-4296-4
    Mathematical Reviews: MR2873804
    Zentralblatt Math: 1239.51003
  14. Properties of codes with two homogeneous weights
    (with Eimear Byrne and Alison Sneyd)
    Finite Fields and Their Applications 18, 4 (2012-7), 711–727.
    Digital Object Identifier: 10.1016/j.ffa.2012.01.002
    arXiv: 1101.4844
    Mathematical Reviews: MR2928466
    Zentralblatt Math: 1245.05135
  15. Minimum weights and weight enumerators of ℤ4-linear quadratic residue codes
    (with Alfred Wassermann)
    IEEE Transactions on Information Theory 58, 7 (2012-7), 4870–4883.
    Digital Object Identifier: 10.1109/TIT.2012.2191389
    Mathematical Reviews: MR2949857
  16. Designs in projective Hjelmslev spaces
    (with Ivan Landjev)
    Contemporary Mathematics 579 (2012), ISBN 978-0-8218-5298-9, 111–121.
    Digital Object Identifier: 10.1090/conm/579/11524
    Mathematical Reviews: MR2975737
    Zentralblatt Math: 1281.51004
  17. New ring-linear codes from dualization in projective Hjelmslev geometries
    (with Johannes Zwanzger)
    Designs, Codes and Cryptography 66, 1–3 (2013-1), 39–55.
    Digital Object Identifier: 10.1007/s10623-012-9650-1
    Mathematical Reviews: MR3016555
    Zentralblatt Math: 1280.94110
  18. Codes from translation schemes on Galois rings of characteristic 4
    Electronic Notes in Discrete Mathematics 40 (2013-5-15), 175–180.
    Digital Object Identifier: 10.1016/j.endm.2013.05.032
  19. There is no self-dual ℤ4-linear code whose Gray image has the parameters (72,236,16)
    IEEE Transactions of Information Theory 59, 6 (2013-6), 3384–3386.
    Digital Object Identifier: 10.1109/TIT.2012.2191389
    Mathematical Reviews: MR3061253
  20. The existence of maximal (q2,2)-arcs in projective Hjelmslev planes over chain rings of length 2 and odd prime characteristic
    (with Thomas Honold)
    Designs, Codes and Cryptography 68, 1–3 (2013-7), 105–126.
    Digital Object Identifier: 10.1007/s10623-012-9653-y
    Mathematical Reviews: MR3046340
    Zentralblatt Math: 1264.05023
  21. On the automorphism group of the binary q-analog of the Fano plane
    (with Michael Braun and Anamari Nakić)
    In Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems. (University of Groningen, July 7–11, 2014), 2014, pp. 1402–1405, ISBN 978-90-367-6321-9.
    pdf-file on conference homepage
  22. Higher-order CIS codes
    (with Claude Carlet, Finley Freibert, Sylvain Guilley, Jon Lark Kim and Patric Solé)
    IEEE Transactions on Information Theory 60, 9 (2014-9), 5283–5295.
    Digital Object Identifier: 10.1109/TIT.2014.2332468
    arXiv: 1406.4547
    Mathematical Reviews: MR3252390
  23. Derived and residual subspace designs
    (with Reinhard Laue)
    Advances in Mathematics of Communications 9, 1 (2015-2), 105–115.
    Digital Object Identifier: 10.3934/amc.2015.9.105
    arXiv: 1405.5432
    Mathematical Reviews: MR3317589
    Zentralblatt Math: 1314.51002
  24. Optimal binary subspace codes of length 6, constant dimension 3 and minimum subspace distance 4
    (with Thomas Honold and Sascha Kurz)
    Contemporary Mathematics 632 (2015), ISBN 978-0-8218-9860-4, 157–176.
    Digital Object Identifier: 10.1090/conm/632/12627
    arXiv: 1311.0464
    Mathematical Reviews: MR3329980
  25. Intersection numbers for subspace designs
    (with Mario Osvin Pavčević)
    Journal of Combinatorial Designs 23, 11 (2015-11), 463–480.
    Digital Object Identifier: 10.1002/jcd.21403
    arXiv: 1405.6110
    Mathematical Reviews: MR3403762
    Zentralblatt Math: 1331.05049
  26. On the automorphism group of a binary q-analog of the Fano plane
    (with Michael Braun and Anamari Nakić)
    European Journal of Combinatorics 51 (2016-1), 443–457.
    Digital Object Identifier: 10.1016/j.ejc.2015.07.014
    arXiv: 1501.07790
    Mathematical Reviews: MR3398870
    Zentralblatt Math: 1321.05017
  27. The automorphism group of an extremal [120, 60, 24] code does not contain elements of order 29
    (with Javier de la Cruz and Alfred Wassermann)
    Designs, Codes and Cryptography 78, 3 (2016-3), 693–702.
    Digital Object Identifier: 10.1007/s10623-014-0025-7
    Mathematical Reviews: 3459219
    Zentralblatt Math: 1333.94064
  28. On putative q-analogues of the Fano plane and related combinatorial structures
    (with Thomas Honold)
    In Dynamical Systems, Number Theory and Applications. A Festschrift in Honor of Armin Leutbecher’s 80th Birthday, edited by T. Hagen, F. Rupp and J. Scheurle. World Scientific, Hackensack, NJ, Mar. 2016, pages 141–175. ISBN: 978-981-4699-86-0.
    Digital Object Identifier: 10.1142/9789814699877_0008
    arXiv: 1504.06688
    Mathematical Reviews: MR3444245
  29. Constructions and bounds for mixed-dimension subspace codes
    (with Thomas Honold and Sascha Kurz)
    Advances in Mathematics of Communications 10, 3 (2016-8), 649–682
    Digital Object Identifier: 10.3934/amc.2016033
    arXiv: 1512.06660
    Mathematical Reviews: MR3543542
  30. Algebraic structures of MRD Codes
    (with Javier de la Cruz, Alfred Wassermann and Wolfgang Willems)
    Advances in Mathematics of Communications 10, 3 (2016-8), 499–510
    Digital Object Identifier: 10.3934/amc.2016021
    arXiv: 1502.02711
    Mathematical Reviews: MR3543530
  31. Large sets of subspace designs
    (with Michael Braun, Axel Kohnert and Reinhard Laue)
    accepted for publication in Journal of Combinatorial Theory, Series A
    Digital Object Identifier: 10.1016/j.jcta.2016.11.004
    arXiv: 1411.7181
  32. New upper bounds on binary linear codes and a ℤ4-code with a better-than-linear Gray image
    (with Alfred Wassermann and Johannes Zwanzger)
    accepted for publication in IEEE Transactions on Information Theory
    arXiv: 1503.03394
  33. Tables of subspace codes
    (with Daniel Heinlein, Sascha Kurz and Alfred Wassermann)
    technical report
    arXiv: 1601.02864
  34. A new series of large sets of subspace designs over the binary field
    (with Reinhard Laue and Alfred Wassermann)
    preprint
    arXiv: 1603.06976
  35. The order of the automorphism group of a binary q-analog of the Fano plane is at most two
    (with Sascha Kurz and Alfred Wassermann)
    preprint
    arXiv: 1605.03853
  36. Classification of large partial plane spreads in PG(6,2) and related combinatorial objects
    (with Thomas Honold and Sascha Kurz)
    preprint
    arXiv: 1606.07655
  37. Partial spreads and vector space partitions
    (with Thomas Honold and Sascha Kurz)
    preprint
    arXiv: 1611.06328

Conference talks (selection)

  1. On q-analogs of the Fano plane
    Network Coding and Designs, Centre for Advanced Academic Studies, Dubrovnik, Croatia, April 4–8, 2016.
    invited talk, 2016-04-04.
    Slides, Conference homepage
  2. Recursive construction of subspace designs
    Algebraic combinatorics and applications (ALCOMA15), Conference in memory of Axel Kohnert, Kloster Banz, Germany, March 15–20, 2015.
    contributed talk, 2015-03-20.
    Slides, Conference homepage
  3. New subspace designs from large set recursion
    Combinatorics 2014, Hotel Serapo, Gaeta, Italy, June 1–6, 2014.
    contributed talk, 2014-06-05.
    Slides, Conference homepage
  4. Intersection numbers for q-analogs of designs
    Conference on random network codes and designs over GF(q), Department of Mathematics of Ghent University, Ghent, Belgium, September 18–20, 2013.
    contributed talk, 2013-09-18.
    Slides, Conference homepage
  5. On the maximum number of planes in PG(𝔽26) whose pairwise intersection is at most a point
    The 11th International Conference on Finite Fields and their Applications (Fq11), Otto-von-Guericke Universität Magdeburg, Germany, July 22–26, 2013.
    contributed talk, 2013-07-23.
    Slides, Conference homepage
  6. New ring-linear codes of high minimum distance
    Trends in Coding Theory, Centro Stefano Franscini, Monte Verità, Ascona, Switzerland, October 28–November 2, 2012.
    contributed talk, 2012-11-01.
    Slides, Conference homepage
  7. Codes from translation schemes on Galois rings of characteristic 4
    Combinatorics 2012, Centro Congressi Hotel Giò, Perugia, Italy, September 9–15, 2012.
    contributed talk, 2012-09-11.
    Slides, Conference homepage

Thesis

Geometrische Konstruktionen linearer Codes über Galois-Ringen der Charakteristik 4 von hoher homogener Minimaldistanz

The following image shows the projective Hjelmslev plane over the integers modulo 4. The black circles indicate a maximal (7,2)-arc, which is unique up to geometric isomorphism. Its Gray image generates the expurgated Nordstrom-Robinson code, a nonlinear binary [14,6,6]-code which has better minimum distance than any linear binary [14,6]-code.
Projective Hjelmslev Plane over Z_4

Miscellaneous

In this preprint we classified the (6,4;3)2 constant dimension subspace codes of maximum possible size. It turned out that the maximum size is 77, and that there are 5 isomorphism classes of those codes:
  1. #Aut = 168, self-dual, list of subspaces
  2. #Aut = 48, self-dual, list of subspaces
  3. #Aut = 2, self-dual, list of subspaces
  4. #Aut = 2, dual code of 5, list of subspaces
  5. #Aut = 2, dual code of 4, list of subspaces