Publications of Anton Betten

Books

  1. A. Betten, H. Fripertinger, A. Kerber, A. Wassermann, K.-H. Zimmermann. Codierungstheorie, Konstruktion und Anwendung Linearer Codes Springer Verlag 1998.
  2. Anton Betten, A. Kohnert, R. Laue, A. Wassermann (eds). Algebraic Combinatorics and Applications Proceedings of the Euroconference Algebraic Combinatorics and Applications (ALCOMA) held in Goessweinstein, Germany, September 12-19, 1999. Springer Verlag 2000, 347+XI.
  3. Anton Betten, Michael Braun, Harald Fripertinger, Adalbert Kerber, Axel Kohnert, Alfred Wassermann. Error-Correcting Linear Codes, Classification by Isometry and Applications, Algorithms and Computation in Mathematics 18, Springer Berlin Heidelberg New York 2006. ISSN 1431-1550. ISBN-10 3-540-28371-4. ISBN-13 978-3-540-28371-3.

Book Chapters

  1. Anton Betten. Partially Balanced Designs as Linear Spaces. In: Handbook of Combinatorial Designs. Second Edition. Charlie Colbourn and Jeff Dinitz (eds.), CRC Press, Boca Raton, 2006. pp. 266-270

Articles and Other Publications

  1. A. Betten, A. Kerber, R. Laue, A. Wassermann. Es gibt 7-Designs mit kleinen Parametern! Es gibt 7-Designs mit kleinen Parametern! Bayreuther Mathematische Schriften 49 (1995), p. 213.
  2. A. Betten, A. Kerber, A. Kohnert, R. Laue, A. Wassermann. Discovery of Simple 7-Designs with Automorphism Group PΓL(2,32), The Discovery of Simple 7-Designs with Automorphism Group $P\Gamma L(2,32)$ Springer LNCS 948 (1995), 131-145.
  3. Anton Betten. Parallel Construction of Finite Solvable Groups, Parallel Construction of Finite Solvable Groups Proceedings EuroPVM'96, TU Munich, Springer Lecture Notes in Computer Science 1156 (1996), 126-133.
  4. A. Betten, A. Wassermann. {0,1}-Solutions of Integer Linear Equation Systems $\{0,1\}$-Solutions of Integer Linear Equation Systems Proceedings EuroPVM'96, TU Munich, Springer Lecture Notes in Computer Science 1156 (1996), 311-314.
  5. Anton Betten, Dieter Betten. Regular Linear Spaces, Regular Linear Spaces Beiträge zur Algebra und Geometrie 38 (1997), 111-124.
  6. A. Betten, R. Laue, A. Wassermann. Some simple 7-designs, Some simple 7-designs In: Geometry, Combinatorial Designs and Related Structures, Proceedings of the First Pythagorean Conference, J. W. P. Hirschfeld, S. S. Magliveras, M. J. de Resmini (eds.) Cambridge University Press, LMS Lecture Notes 245 (1997), 15-25.
  7. A. Betten, R. Laue, A. Wassermann. Simple 6- and 7-designs on 19 to 33 points, Simple 6- and 7-designs on 19 to 33 points Congressus Numerantium 123 (1997), 149-160.
  8. A. Betten, M. Klin, R. Laue, C. Pech. A computer approach to the enumeration of block designs which are invariant with respect to a prescribed permutation group, Universität Dresden, preprint MATH-AL-13-1997, November 1997, 74 pages.
  9. Anton Betten, Reinhard Laue, Adalbert Kerber, Alfred Wassermann. Simple 8-Designs with Small Parameters, Simple 8-Designs with Small Parameters Designs, Codes, Cryptography 15 (1998), 5-27.
  10. Anton Betten, Reinhard Laue, Alfred Wassermann. Simple 7-Designs With Small Parameters, Simple 7-Designs With Small Parameters Journal of Combinatorial Designs 7 (1999), 79-94.
  11. Anton Betten, Dieter Betten. Linear spaces with at most 12 points, Linear spaces with at most 12 points Journal of Combinatorial Designs 7 (1999), 119-145.
  12. A. Betten, R. Laue, A. Wassermann. New t-designs and large sets of t-designs, New t-designs and large sets of t-designs Presented at BCC16, London 1997. Discrete Mathematics 197/198 (1999), 111-121.
  13. A. Betten, M.C. Klin, R. Laue, A. Wassermann. Graphical t-Designs via Polynomial Kramer-Mesner Matrices, Graphical t-Designs via Polynomial Kramer-Mesner Matrices Presented at BCC16, London 1997. Discrete Mathematics 197/198 (1999), 83-109.
  14. Anton Betten, Dieter Betten. Proper Linear Spaces on 17 Points, The Proper Linear Spaces on 17 Points Discrete Applied Mathematics 95 (1999), 83-108.
  15. A. Betten, R. Laue, A. Wassermann. Simple 8-(40,11,1440) Designs, Simple 8-(40,11,1440) Designs Presented at ODSA, Rostock 1997. Discrete Applied Mathematics 95 (1999), 109-114.
  16. A. Betten, R. Laue, A. Wassermann. A Steiner 5-Design on 36 Points, A Steiner 5-Design on 36 Points Designs, Codes and Cryptography 17 (1999), 181-186.
  17. Anton Betten, Dieter Betten. Tactical decompositions and some configurations v4, Tactical decompositions and some configurations v4 Journal of Geometry 66 (1999), 27-41.
  18. Anton Betten, Gunnar Brinkmann, Thomasz Pisanski. Counting symmetric configurations v3, Counting symmetric configurations v3 Discrete Applied Mathematics 99 (2000), 331-338.
  19. A. Betten, C. Alejandro, A. Niemeyer. Orderly Generation of Half-Regular Symmetric Designs via Rahilly Families of Pre-Difference Sets, Orderly Generation of Half-Regular Symmetric Designs via Rahilly Families of Pre-Difference Sets Journal of Geometry 67 (2000), 2-22.
  20. A. Betten, R. Laue, S. Molodtsov, A. Wassermann. Steiner Systems with Automorphism Groups PSL(2,71), PSL(2,83) and P ΣL(2,35), Steiner Systems with Automorphism Groups PSL(2,71), PSL(2,83) and $P \Sigma L(2,3^5)$ Journal of Geometry 67 (2000), 35-41.
  21. Anton Betten, Schnittzahlen von Designs, Schnittzahlen von Designs (English translation: Intersection Numbers of Designs) Thesis, University of Bayreuth. Bayreuther Mathematische Schriften 58 (2000), x:1-131.
  22. Anton Betten, Dieter Betten. Note on the Proper Linear Spaces on 18 Points, Note on the Proper Linear Spaces on 18 Points Proceedings of ALCOMA 1999, Springer Verlag 2000, 40-54.
  23. Evi Haberberger, Anton Betten, Reinhard Laue. Isomorphism Classification of t-Designs with Grouptheoretical Localisation Techniques Applied to some Steiner Quadrupel Systems on 20 Points, Isomorphism Classification of t-Designs with Grouptheoretical Localisation Techniques Applied to some Steiner Quadrupel Systems on 20 Points Congressus Numerantium 142 (2000), 75-96.
  24. Reinhard Laue, Anton Betten, Evi Haberberger. A New Smallest Simple 6-Design With Automorphism Group A4, A New Smallest Simple 6-Design With Automorphism Group A4 Congressus Numerantium 150 (2001), 145-153.
  25. Anton Betten, Dieter Betten, Vladimir Tonchev. Unitals and Codes, Unitals and Codes Discrete Mathematics 267 (2003) 23-33.
  26. Anton Betten, Reinhard Laue, Alfred Wassermann. DISCRETA, a tool for constructing t-designs In: Computer Algebra Handbook, Edited by Johannes Grabmeier, Erich Kaltofen, Volker Weispfennig, Springer 2003, pp 372-375.
  27. Anton Betten, Anne Delandtsheer, Alice C. Niemeyer, Cheryl E. Praeger. On a theorem of Wielandt for finite primitive permutation groups, On a theorem of Wielandt for finite primitive permutation groups Journal of Group Theory 6 (2003), 415-420.
  28. Anton Betten. Genealogy of t-designs, Genealogy of t-designs The Australasian Journal of Combinatorics 29 (2004) 3-34.
  29. Anton Betten, Dieter Betten. More on Regular Linear Spaces, More on Regular Linear Spaces Journal of Combinatorial Designs 13 (2005) 441-461.
  30. Anton Betten, Gregory Cresp, Alice C. Niemeyer, Cheryl E. Praeger. A search algorithm for line-transitive, point-imprimitive linear spaces, A search algorithm for line-transitive, point-imprimitive linear spaces Bayreuther Mathematische Schriften 74 (2005) 42-57.
  31. Anton Betten. Geometric Codes and Hyperovals, Geometric Codes and Hyperovals Bayreuther Mathematische Schriften 74 (2005) 19-41.
  32. Anton Betten, Computing Linear Codes and Orbits on Sets. Workshop: Computational Group Theory, Organized by Gerhard Hiss, Derek Holt, Mike Newman. July 2 - July 8 2006. Oberwolfach Report 30/2006, 12-14.
  33. A. Betten, R. J. Kingan, S. R. Kingan. A Note on GF(5)-Representable Matroids, MATCH Commun. Math. Comput. Chem. 58 (2007) 511-521.
  34. Anton Betten, Greg Cresp, Cheryl E. Praeger. Line-transitive point-imprimitive linear spaces: the grid case, Innovations in Incidence Geometry 8 (2008) 117-135.
  35. Anton Betten, Twisted Tensor Product Codes. Twisted Tensor Product Codes Designs, Codes and Cryptography 47 (2008), no 1-3, 191-219.
  36. Anton Betten, Anne Delandtsheer, Maska Law, Alice C. Niemeyer, Cheryl E. Praeger, Shenglin Zhou. Finite line-transitive linear spaces: theory and search strategies, Acta Mathematica Sinica, English Series, Sep., 2009, Vol. 25, No. 9, pp. 1399-1436.
  37. Anton Betten, Dieter Betten. There is no Drake / Larson linear space on 30 points, There is no Drake / Larson linear space on $30$ points Journal of Combinatorial Designs, 18: 48-70, 2010.
  38. Anton Betten. A class of transitive BLT-sets. A class of transitive BLT-sets. Note di Matematica 28 (2010), 2-10.
  39. Abdullah Al-Azemi, Anton Betten. Classification of Triangle-Free 223-Configurations. Classification of Triangle-Free $22_3$-Configurations. International Journal of Combinatorics, Volume 2010 (2010), Article Id 767361, 17 Pages.
  40. Anton Betten, Eun Ju Cheon, Seon Jeong Kim, Tatsuya Maruta. The Classification of (42,6)8 Arcs. The Classification of $(42,6)_8$ Arcs. Advances in Mathematics of Communication 5 (2011), 209-223.
  41. Anton Betten, Eun Ju Cheon, Seon Jeong Kim, Tatsuya Maruta. Three Families of Multiple Blocking Sets in Desarguesian Projective Planes of Even Order. Designs, Codes, Cryptography 68 (2013), no. 1-3, 49-59.
  42. Anton Betten. Rainbow Cliques and the Classification of Small BLT-Sets. ISSAC' 13, June 26-29, 2013, Boston, Massachusetts. Ed. Manuel Kauers. 53-60.
  43. Abdullah Al-Azemi, Anton Betten, Dieter Betten. Unital Designs with Blocking Set. Discrete Applied Mathematics 163 (2014), no 1, 102-112
  44. John Bamberg, Anton Betten, Cheryl Praeger, Alfred Wassermann. Unitals in the Desarguesian Projective Plane of Order 16. Journal of Statistical Planning and Inference 144 (2014), no 1, 110-122.
  45. Anton Betten. Classifying Discrete Objects with Orbiter. ACM Communications in Computer Algebra 01/2014; 47(3/4):183-186. DOI:10.1145/2576802.2576832
  46. Anton Betten. The packings of PG(3,3). Des. Codes Cryptogr. 79 (2016), no. 3, 583-595.
  47. Anton Betten, Alfred Wassermann. Spreads of PG(3,8) and PG(3,9) containing a regulus. Congressus Numerantium 226 (2016), 289-299.
  48. Anton Betten, Ulrich Dempwolff, Alfred Wassermann. On Dual Hyperovals of Rank 4 Over \mathbb F2. Journal of Geometry 108 (2017), no. 1, 75-98.
  49. Anton Betten, James W. P. Hirschfeld, Fatma Karaoglu. Classification of cubic surfaces with twenty-seven lines over the finite field of order thirteen. Eur. J. Math. 4 (2018), no. 1, 37–-50.
  50. Abdullah Al-Azemi, Anton Betten, and Sajeeb Roy Chowdhury. A rainbow-clique search algorithm for BLT-sets. In ICMS 2018-Proceedings of the International Congress on Mathematical Software; James H. Davenport, Manuel Kauers, George Labahn, Josef Urban (ed.), pages 71-79. Springer, 2018.
  51. Anton Betten. Classifying cubic surfaces over finite fields using orbiter. In ICMS 2018-Proceedings of the International Congress on Mathematical Software; James H. Davenport, Manuel Kauers, George Labahn, Josef Urban (ed.), pages 55-61. Springer, 2018.
  52. Anton Betten. How fast can we compute orbits of groups? In ICMS 2018-Proceedings of the International Congress on Mathematical Software; James H. Davenport, Manuel Kauers, George Labahn, Josef Urban (ed.), pages 62-70. Springer, 2018.
  53. Anton Betten, Svetlana Topalova, and Stela Zhelezova. Parallelisms of PG(3,4) invariant under a Baer involution. Sixteenth International Workshop on Algebraic and Combinatorial Coding Theory ACCT XVI. September 2-8, 2018. Svertlogorsk near Kaliningrad. acct2018.skoltech.ru.
  54. Anton Betten, Fatma Karaoglu. Cubic Surfaces Over Small Finite Fields. Des. Codes Cryptogr. (2019) 87: 931-953.
  55. Anton Betten, Svetlana Topalova, and Stela Zhelezova. Parallelisms of PG(3,4) invariant under cyclic groups of order four. M. Círić et al. (Eds.): CAI 2019, Springer LNCS 11545, pp. 88–99, 2019.
  56. Anton Betten. Poset Classification and Optimal Linear Codes. Submitted to Mathematics in Computer Science.
  57. Anton Betten, Awss Al-ogaidi. Large Arcs in Small Planes. Submitted to Congressus Numerantium.
  58. Anton Betten, Fatma Karaoglu. The Number of Cubic Surfaces with 27 Lines Over a Finite Field. Submitted to Journal of Algebraic Combinatorics.
  59. Anton Betten, Fatma Karaoglu. The Hilbert Cohn-Vossen cubic surface. Submitted.
  60. Anton Betten, Eun Ju Cheon, Seon Jeong Kim, Tatsuya Maruta. The (33,5)-Arcs in PG(2,8). Submitted to Electronic Journal of Combinatorics.
  61. Anton Betten, Sajeeb Roy Chowdhury. Optimizing Schreier Trees with Machine Learning Extended abstract; accepted for a presentation at The 13th International Conference on Multiple Objective Programming and Goal Programming in 2019 in Marrakesh, Marocco.


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