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.

ORCID iD iconhttps://orcid.org/0000-0002-5901-4381

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
    ERef Bayreuth: 3901
  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 (reviewed by Hubert Kiechle (Hamburg))
    ERef Bayreuth: 3281
  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
    Zentralblatt Math: 1366.94743
    ERef Bayreuth: 3736
  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 (reviewed by Plamen Koshlukov (Campinas))
    ERef Bayreuth: 3735
  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. ERef Bayreuth: 3902
  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)
    ERef Bayreuth: 3903
  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, special issue ALCOMA'10), 275–286.
    Digital Object Identifier: 10.3934/amc.2011.5.275
    Mathematical Reviews: MR2801593 (reviewed by Giorgio Faina)
    Zentralblatt Math: 1252.94120
    ERef Bayreuth: 3734
  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, special issue ALCOMA'10), 287–301.
    Digital Object Identifier: 10.3934/amc.2011.5.287
    arXiv: 1401.4340
    Mathematical Reviews: MR2801594 (reviewed by Giorgio Faina)
    Zentralblatt Math: 1228.51006
    ERef Bayreuth: 3421
  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 (reviewed by Andrea Blunck)
    Zentralblatt Math: 1239.51003
    ERef Bayreuth: 3733
  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
    ERef Bayreuth: 3731
  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
    Zentralblatt Math: 1365.94518
    ERef Bayreuth: 3730
  16. Designs in projective Hjelmslev spaces
    (with Ivan Landjev)
    In Theory and Applications of Finite Fields: The 10th International Conference on Finite Fields and Their Applications, July 11–15, 2011, Ghent, Belgium, pages 111–121. Edited by Michel Lavrauw, Gary L. Mullen, Svetla Nikova, Daniel Panario and Leo Storme. Contemporary Mathematics 579. American Mathematical Society, Providence, Rhode Island, 2012. ISBN 978-0-8218-5298-9
    Digital Object Identifier: 10.1090/conm/579/11524
    Mathematical Reviews: MR2975737 (reviewed by Andrea Blunck)
    Zentralblatt Math: 1281.51004
    ERef Bayreuth: 3728
  17. New ring-linear codes from dualization in projective Hjelmslev geometries
    (with Johannes Zwanzger)
    Designs, Codes and Cryptography 66, 1–3 (2013-1, special issue on Coding and Cryptography), 39–55.
    Digital Object Identifier: 10.1007/s10623-012-9650-1
    Mathematical Reviews: MR3016555 (reviewed by Edgar Martínez-Moro)
    Zentralblatt Math: 1280.94110
    ERef Bayreuth: 3727
  18. Codes from translation schemes on Galois rings of characteristic 4
    Electronic Notes in Discrete Mathematics 40 (2013-5-15, Combinatorics 2012), 175–180.
    Digital Object Identifier: 10.1016/j.endm.2013.05.032
    ERef Bayreuth: 3725
  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
    Zentralblatt Math: 1364.94613
    ERef Bayreuth: 3717
  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, special issue: Finite Geometries), 105–126.
    Digital Object Identifier: 10.1007/s10623-012-9653-y
    Mathematical Reviews: MR3046340 (reviewed by Joanne Lesley Hall)
    Zentralblatt Math: 1264.05023
    ERef Bayreuth: 3716
  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
    ERef Bayreuth: 32157
  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
    Zentralblatt Math: 1360.94362
    ERef Bayreuth: 3644
  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 (reviewed by Jianguo Lei)
    Zentralblatt Math: 1314.51002
    ERef Bayreuth: 7585
  24. Optimal binary subspace codes of length 6, constant dimension 3 and minimum subspace distance 4
    (with Thomas Honold and Sascha Kurz)
    In Topics in Finite Fields: Proceedings of the 11th International Conference on Finite Fields and their Applications (Fq11) held in Magdeburg, July 22–26, 2013, pages 157–176. Edited by Gohar Kyureghyan, Gary L. Mullen and Alexander Pott. Contemporary Mathematics 632. American Mathematical Society, Providence, Rhode Island, 2015. ISBN 978-0-8218-9860-4
    Digital Object Identifier: 10.1090/conm/632/12627
    arXiv: 1311.0464
    Mathematical Reviews: MR3329980 (reviewed by Jonathan I. Hall)
    Zentralblatt Math: 1355.94094
    ERef Bayreuth: 7922
  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
    ERef Bayreuth: 32032
  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 (reviewed by Jennifer D. Key)
    Zentralblatt Math: 1321.05017
    ERef Bayreuth: 32031
  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 (reviewed by José María Ancochea Bermúdez)
    Zentralblatt Math: 1333.94064
    ERef Bayreuth: 32030
  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 (reviewed by Metod Saniga)
    Zentralblatt Math: 1357.51004 (reviewed by Hans-Peter Schröcker (Innsbruck))
    ERef Bayreuth: 32156
  29. Constructions and bounds for mixed-dimension subspace codes
    (with Thomas Honold and Sascha Kurz)
    Advances in Mathematics of Communications 10, 3 (2016-8, special issue on ALCOMA'15), 649–682
    Digital Object Identifier: 10.3934/amc.2016033
    arXiv: 1512.06660
    Mathematical Reviews: MR3543542
    Zentralblatt Math: 06637568
    ERef Bayreuth: 34825
  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, Special issue on ALCOMA'15), 499–510
    Digital Object Identifier: 10.3934/amc.2016021
    arXiv: 1502.02711
    Mathematical Reviews: MR3543530 (reviewed by K. T. Phelps)
    Zentralblatt Math: 1348.94102
    ERef Bayreuth: 34623
  31. New upper bounds on binary linear codes and a ℤ4-code with a better-than-linear Gray image
    (with Alfred Wassermann and Johannes Zwanzger)
    IEEE Transactions on Information Theory 62, 12 (2016-12), 6768–6771
    Digital Object Identifier: 10.1109/TIT.2016.2612654
    arXiv: 1503.03394
    Mathematical Reviews: MR3578230 (reviewed by K. T. Phelps)
    Zentralblatt Math: 1359.94707
    ERef Bayreuth: 36947
  32. Large sets of subspace designs
    (with Michael Braun, Axel Kohnert and Reinhard Laue)
    Journal of Combinatorial Theory, Series A 147 (2017-4), 155–185
    Digital Object Identifier: 10.1016/j.jcta.2016.11.004
    arXiv: 1411.7181
    Mathematical Reviews: MR3589893 (reviewed by Anamari Nakić)
    Zentralblatt Math: 1352.05042
    ERef Bayreuth: 36946
  33. Tables of subspace codes
    (with Daniel Heinlein, Sascha Kurz and Alfred Wassermann)
    technical report
    arXiv: 1601.02864
  34. Projective divisible binary codes
    (with Daniel Heinlein, Thomas Honold, Sascha Kurz and Alfred Wassermann)
    In Proceedings of The Tenth International Workshop on Coding and Cryptography 2017, September 18-22, 2017, Saint-Petersburg, Russia, 2017
    pdf-file on conference homepage
    arXiv: 1703.08291
    ERef Bayreuth: 40887
  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)
    Designs, Codes and Cryptography 86, 2 (2018-2, special issue on Network Coding and Designs), 239–250
    Digital Object Identifier: 10.1007/s10623-017-0360-6
    arXiv: 1605.03853
    Mathematical Reviews: MR3756140 (reviewed by Anamari Nakić)
    Zentralblatt Math: 1394.51002 (reviewed by Leo Storme (Gent))
    ERef Bayreuth: 42175
  36. A new series of large sets of subspace designs over the binary field
    (with Reinhard Laue and Alfred Wassermann)
    Designs, Codes and Cryptography 86, 2 (2018-2, special issue on Network Coding and Designs), 251–268
    Digital Object Identifier: 10.1007/s10623-017-0349-1
    arXiv: 1603.06976
    Mathematical Reviews: MR3756141 (reviewed by W. M. Kantor)
    Zentralblatt Math: 1379.05018
    ERef Bayreuth: 44593
  37. Partial spreads and vector space partitions
    (with Thomas Honold and Sascha Kurz)
    In Network Coding and Subspace Designs, pages 131–170. Edited by Marcus Greferath, Mario Osvin Pavčević, Natalia Silberstein and María Ángeles Vázquez-Castro. Signals and Communication Theory, Springer, Cham, 2018. ISBN 978-3-319-70292-6
    Digital Object Identifier: 10.1007/978-3-319-70293-3_7
    arXiv: 1611.06328
    Mathematical Reviews: MR3586132 (reviewed by Jonathan I. Hall)
    ERef Bayreuth: 42176
  38. q-analogs of designs: Subspace designs
    (with Michael Braun and Alfred Wassermann)
    In Network Coding and Subspace Designs, pages 171–211. Edited by Marcus Greferath, Mario Osvin Pavčević, Natalia Silberstein and María Ángeles Vázquez-Castro. Signals and Communication Theory, Springer, Cham, 2018. ISBN 978-3-319-70292-6
    Digital Object Identifier: 10.1007/978-3-319-70293-3_8
    Mathematical Reviews: MR3586133 (reviewed by Anamari Nakić)
    ERef Bayreuth: 44594
  39. Computational methods in subspace designs
    (with Michael Braun and Alfred Wassermann)
    In Network Coding and Subspace Designs, pages 213–244. Edited by Marcus Greferath, Mario Osvin Pavčević, Natalia Silberstein and María Ángeles Vázquez-Castro. Signals and Communication Theory, Springer, Cham, 2018. ISBN 978-3-319-70292-6
    Digital Object Identifier: 10.1007/978-3-319-70293-3_9
    Mathematical Reviews: MR3586134
    ERef Bayreuth: 44595
  40. Generalized vector space partitions
    (with Daniel Heinlein, Thomas Honold and Sascha Kurz)
    The Australasian Journal of Combinatorics 73, 1 (2019), 162–178
    Journal link (open access)
    arXiv: 1803.10180
    Mathematical Reviews: MR3884516 (review pending)
    ERef Bayreuth: 46411
  41. New 2-designs over finite fields from derived and residual designs
    (with Michael Braun and Reinhard Laue)
    Advances in Mathematics of Communications 13, 1 (2019-2), 165–170
    Digital Object Identifier: 10.3934/amc.2019010
    Mathematical Reviews: MR3917654 (review pending)
    ERef Bayreuth: 46749
  42. Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6
    (with Daniel Heinlein, Thomas Honold, Sascha Kurz and Alfred Wassermann)
    Designs, Codes and Cryptography 87, 2–3 (2019-3, special issue: Coding and Cryptography), 375–391
    Digital Object Identifier: 10.1007/s10623-018-0544-8
    arXiv: 1711.06624
    Mathematical Reviews: MR3911211 (review pending)
    ERef Bayreuth: 46984
  43. Classification of large partial plane spreads in PG(6,2) and related combinatorial objects
    (with Thomas Honold and Sascha Kurz)
    Journal of Geometry 110, 1 (2019-4), Art. 5, 31pp.
    Digital Object Identifier: 10.1007/s00022-018-0459-6
    arXiv: 1606.07655
    Mathematical Reviews: MR3891806 (review pending)
    ERef Bayreuth: 46673
  44. A subspace code of size 333 in the setting of a binary q-analog of the Fano plane
    (with Daniel Heinlein, Sascha Kurz and Alfred Wassermann)
    Advances in Mathematics of Communications 13, 3 (2019-8), 393–404
    Digital Object Identifier: 10.3934/amc.2019029
    arXiv: 1708.06224
  45. An improvement of the Johnson bound for subspace codes
    (with Sascha Kurz)
    preprint
    arXiv: 1707.00650
  46. q-analogs of group divisible designs
    (with Marco Buratti, Sascha Kurz, Anamari Nakić and Alfred Wassermann)
    preprint
    arXiv: 1804.11172
  47. The lengths of projective triply-even binary codes
    (with Thomas Honold, Sascha Kurz and Alfred Wassermann)
    preprint
    arXiv: 1812.05957

Conference talks (selection)

  1. On the lengths of divisible codes
    Oberwolfach Workshop 1912: Contemporary Coding Theory, Mathematisches Forschungsinstitut Oberwolfach, Germany, March 18–22, 2019.
    contributed talk, 2019-03-21.
    Slides, Conference homepage
  2. On the lengths of divisible codes
    Kolloquium über Kombinatorik (Colloquium on Combinatorics, KolKom), Paderborn University, Germany, November 23–24, 2018.
    contributed talk, 2018-11-24.
    Slides, Conference homepage
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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