Combinatorics

Designs and Configurations

05Bxx

  1. David Applegate, E. M. Rains, and N. J. A. Sloane, On asymmetric coverings and covering numbers, J. Combin. Des. 11 (2003), no. 3, 218–228.[MR]
  2. Makoto Araya, Masaaki Harada, and Hadi Kharaghani, Some Hadamard matrices of order 32 and their binary codes, J. Combin. Des. 12 (2004), no. 2, 142–146.[MR]
  3. E. F. Assmus, Jr. and J. D. Key, Translation planes and derivation sets, J. Geom. 37 (1990), no. 1-2, 3–16.[MR]
  4. E. F. Assmus, Jr. and J. D. Key, Hadamard matrices and their designs: A coding-theoretic approach, Trans. Amer. Math. Soc. 330 (1992), no. 1, 269–293.[MR]
  5. R. A. Bailey, Peter J. Cameron, Peter Dobcsányi, John P. Morgan, and Leonard H. Soicher, Designs on the web, Discrete Math. 306 (2006), no. 23, 3014–3027.[MR]
  6. John Bamberg and Tim Penttila, A classification of transitive ovoids, spreads, and m-systems of polar spaces, Forum Math. 21 (2009), no. 2, 181–216.[MR]
  7. Eiichi Bannai and Etsuko Bannai, On Euclidean tight 4-designs, J. Math. Soc. Japan 58 (2006), no. 3, 775–804.[MR]
  8. L. M. Batten and J. M. Dover, Some sets of type (m,n) in cubic order planes, Des. Codes Cryptogr. 16 (1999), no. 3, 211–213.[MR]
  9. Thomas Beth, Christopher Charnes, Markus Grassl, Gernot Alber, Aldo Delgado, and Michael Mussinger, A new class of designs which protect against quantum jumps, Des. Codes Cryptogr. 29 (2003), no. 1-3, 51–70.[MR]
  10. Anton Betten, Adalbert Kerber, Reinhard Laue, and Alfred Wassermann, Simple 8-designs with small parameters, Des. Codes Cryptogr. 15 (1998), no. 1, 5–27.[MR]
  11. A. Bonnecaze, E. Rains, and P. Solé, 3-colored 5-designs and Z4-codes, J. Statist. Plann. Inference 86 (2000), no. 2, 349–368.[MR]
  12. A. Bonnecaze, P. Solé, and P. Udaya, Tricolore 3-designs in type III codes, Discrete Math. 241 (2001), no. 1-3, 129–138.[MR]
  13. Alexis Bonnecaze, Bernard Mourrain, and Patrick Solé, Jacobi polynomials, type II codes, and designs, Des. Codes Cryptogr. 16 (1999), no. 3, 215–234.[MR]
  14. Thomas Britz and Carrie G. Rutherford, Covering radii are not matroid invariants, Discrete Math. 296 (2005), no. 1, 117–120.[MR]
  15. Thomas Britz and Keisuke Shiromoto, Designs from subcode supports of linear codes, Des. Codes Cryptogr. 46 (2008), no. 2, 175–189.[MR]
  16. S. Allen Broughton, Robert M. Dirks, Maria T. Sloughter, and C. Ryan Vinroot, Triangular surface tiling groups for low genus, Preprint (2001).
  17. F. Buekenhout, A. Delandtsheer, and J. Doyen, Finite linear spaces with flag-transitive groups, J. Combin. Theory Ser. A 49 (1988), no. 2, 268–293.[MR]
  18. A. R. Camina and L. Di Martino, Block designs on 196 points, Arch. Math. (Basel) 53 (1989), no. 4, 414–416.[MR]
  19. A. R. Camina and L. Di Martino, The group of automorphisms of a transitive 2-(91,6,1) design, Geom. Dedicata 31 (1989), no. 2, 151–164.[MR]
  20. I. Cardinali, N. Durante, T. Penttila, and R. Trombetti, Bruen chains over fields of small order, Discrete Math. 282 (2004), no. 1-3, 245–247.[MR]
  21. L. L. Carpenter and J. D. Key, On Hadamard matrices from resolvable Steiner designs, in Proceedings of the Twenty-sixth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1995), vol. 108, 1995, pp. 53–63.[MR]
  22. David B. Chandler and Qing Xiang, Cyclic relative difference sets and their p-ranks, Des. Codes Cryptogr. 30 (2003), no. 3, 325–343.[MR]
  23. Chris Charnes, Martin Rötteler, and Thomas Beth, Homogeneous bent functions, invariants, and designs, Des. Codes Cryptogr. 26 (2002), no. 1-3, 139–154.[MR]
  24. D. Combe, W. D. Palmer, and W. R. Unger, Bhaskar Rao designs and the alternating group A4, Australas. J. Combin. 24 (2001), 275–283.[MR]
  25. Marston Conder and John McKay, Markings of the Golay code, New Zealand J. Math. 25 (1996), no. 2, 133–139.[MR]
  26. Antonio Cossidente and Sam K. J. Vereecke, Some geometry of the isomorphism Sp(4,q)≅O(5,q), q even, J. Geom. 70 (2001), no. 1-2, 28–37.[MR]
  27. M. R. Darafsheh, A. Iranmanesh, and R. Kahkeshani, Some designs and codes invariant under the groups S9 and A8, Des. Codes Cryptogr. 51 (2009), no. 2, 211–223.[MR/doi]
  28. U. Dempwolff, Automorphisms and equivalence of bent functions and of difference sets in elementary abelian 2-groups, Comm. Algebra 34 (2006), no. 3, 1077–1131.[MR]
  29. Cunsheng Ding, Zeying Wang, and Qing Xiang, Skew Hadamard difference sets from the Ree-Tits slice symplectic spreads in PG(3,32h+1), J. Combin. Theory Ser. A 114 (2007), no. 5, 867–887.[MR/arXiv]
  30. Cunsheng Ding and Jin Yuan, A family of skew Hadamard difference sets, J. Combin. Theory Ser. A 113 (2006), no. 7, 1526–1535.[MR]
  31. G. L. Ebert, Quasimultiples of geometric designs, Discrete Math. 284 (2004), no. 1-3, 123–129.[MR]
  32. Ronald Evans, Henk D. L. Hollmann, Christian Krattenthaler, and Qing Xiang, Gauss sums, Jacobi sums, and p-ranks of cyclic difference sets, J. Combin. Theory Ser. A 87 (1999), no. 1, 74–119.[MR]
  33. Tao Feng, Non-abelian skew hadamard difference sets fixed by a prescribed automorphism, J Combin. Theory Ser. A, to appear (2009).[doi]
  34. W. Fish, J. D. Key, and E. Mwambene, Graphs, designs and codes related to the n-cube, Discrete Math. 309 (2009), no. 10, 3255–3269.[MR]
  35. D. L. Flannery, Cocyclic Hadamard matrices and Hadamard groups are equivalent, J. Algebra 192 (1997), no. 2, 749–779.[MR]
  36. Anna Fukshansky and Corinna Wiedorn, C-extensions of the Petersen geometry for M22, European J. Combin. 20 (1999), no. 3, 233–238.[MR]
  37. S. Georgiou, I. Kotsireas, and C. Koukouvinos, Inequivalent Hadamard matrices of order 2n constructed from Hadamard matrices of order n, J. Combin. Math. Combin. Comput. 63 (2007), 65–79.[MR]
  38. S. Georgiou and C. Koukouvinos, Some results on orthogonal designs and Hadamard matrices, Int. J. Appl. Math. 17 (2005), no. 4, 433–443.[MR]
  39. Stelios D. Georgiou, New two-variable full orthogonal designs and related experiments with linear regression models, Statist. Probab. Lett. 77 (2007), no. 1, 25–31.[MR]
  40. Claudia Gohlisch, Helmut Koch, and Gabriele Nebe, Block squares, Math. Nachr. 241 (2002), 73–102.[MR]
  41. Ken Gray, On the minimum number of blocks defining a design, Bull. Austral. Math. Soc. 41 (1990), no. 1, 97–112.[MR]
  42. Masaaki Harada, On the self-dual F5-codes constructed from Hadamard matrices of order 24, J. Combin. Des. 13 (2005), no. 2, 152–156.[MR]
  43. Masaaki Harada, Self-orthogonal 3-(56,12,65) designs and extremal doubly-even self-dual codes of length 56, Des. Codes Cryptogr. 38 (2006), no. 1, 5–16.[MR]
  44. Masaaki Harada, Clement Lam, and Vladimir D. Tonchev, Symmetric (4,4)-nets and generalized Hadamard matrices over groups of order 4, Des. Codes Cryptogr. 34 (2005), no. 1, 71–87.[MR]
  45. Masaaki Harada and Akihiro Munemasa, A quasi-symmetric 2-(49,9,6) design, J. Combin. Des. 10 (2002), no. 3, 173–179.[MR]
  46. Masaaki Harada and Vladimir D. Tonchev, Self-orthogonal codes from symmetric designs with fixed-point-free automorphisms, Discrete Math. 264 (2003), no. 1-3, 81–90.[MR]
  47. K. J. Horadam, An introduction to cocyclic generalised Hadamard matrices, Discrete Appl. Math. 102 (2000), no. 1-2, 115–131.[MR]
  48. K. J. Horadam, Hadamard matrices and their applications, Princeton University Press, Princeton, NJ, 2007, pp. xiv+263.[MR]
  49. Naoyuki Horiguchi, Hiroyuki Nakasora, and Takehisa Wakabayashi, On the strongly regular graphs obtained from quasi-symmetric 2-(31,7,7) designs, Bull. Yamagata Univ. Natur. Sci. 16 (2005), no. 1, 1–6.[MR]
  50. Masakazu Jimbo and Keisuke Shiromoto, A construction of mutually disjoint Steiner systems from isomorphic Golay codes, J. Combin. Theory Ser. A 116 (2009), no. 7, 1245–1251.[MR/doi]
  51. G. A. Kadir and J. D. Key, The Steiner system S(5,8,24) constructed from dual affine planes, Proc. Roy. Soc. Edinburgh Sect. A 103 (1986), no. 1-2, 147–160.[MR]
  52. Wen-Fong Ke, On nonisomorphic BIBD with identical parameters, Combinatorics '90 (Gaeta, 1990), Ann. Discrete Math., vol. 52, North-Holland, Amsterdam, 1992, pp. 337–346.[MR]
  53. J. D. Key, Extendable Steiner designs, Geom. Dedicata 41 (1992), no. 2, 201–205.[MR]
  54. J. D. Key, On a class of 1-designs, European J. Combin. 14 (1993), no. 1, 37–41.[MR]
  55. J. D. Key, Extendable Steiner designs from finite geometries, J. Statist. Plann. Inference 56 (1996), no. 2, 181–186.[MR]
  56. J. D. Key and K. Mackenzie, Ovals in the designs W(2m), Ars Combin. 33 (1992), 113–117.[MR]
  57. J. D. Key and K. Mackenzie-Fleming, Rigidity theorems for a class of affine resolvable designs, J. Combin. Math. Combin. Comput. 35 (2000), 147–160.[MR]
  58. J. D. Key, T. P. McDonough, and V. C. Mavron, Partial permutation decoding for codes from finite planes, European J. Combin. 26 (2005), no. 5, 665–682.[MR]
  59. J. D. Key and J. Moori, Codes, designs and graphs from the Janko groups J1 and J2, J. Combin. Math. Combin. Comput. 40 (2002), 143–159.[MR]
  60. J. D. Key and M. J. de Resmini, Small sets of even type and codewords, J. Geom. 61 (1998), no. 1-2, 83–104.[MR]
  61. J. D. Key and F. D. Shobe, Some transitive Steiner triple systems of Bagchi and Bagchi, J. Statist. Plann. Inference 58 (1997), no. 1, 79–86.[MR]
  62. J. D. Key and F. E. Sullivan, Codes of Steiner triple and quadruple systems, Des. Codes Cryptogr. 3 (1993), no. 2, 117–125.[MR]
  63. J. D. Key and F. E. Sullivan, Steiner triple systems with many affine hyperplanes, in Proceedings of the Twenty-sixth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1995), vol. 107, 1995, pp. 105–112.[MR]
  64. Michael Kiermaier and Sascha Kurz, Maximal integral point sets in affine planes over finite fields, Discrete Math. 309 (2009), no. 13, 4564–4575.[MR]
  65. Jon-Lark Kim and Vera Pless, Designs in additive codes over GF(4), Des. Codes Cryptogr. 30 (2003), no. 2, 187–199.[MR]
  66. Jon-Lark Kim and Patrick Solé, Skew Hadamard designs and their codes, Des. Codes Cryptogr. 49 (2008), no. 1-3, 135–145.[MR]
  67. I. S. Kotsireas and C. Koukouvinos, Inequivalent hadamard matrices from orthogonal designs, in PASCO '07: Proceedings of the 2007 International Workshop on Parallel Symbolic Computation, ACM, New York, NY, USA, 2007, pp. 95–96.[doi]
  68. Ilias S. Kotsireas and Christos Koukouvinos, Constructions for Hadamard matrices of Williamson type, J. Combin. Math. Combin. Comput. 59 (2006), 17–32.[MR]
  69. Ilias S. Kotsireas and Christos Koukouvinos, Orthogonal designs via computational algebra, J. Combin. Des. 14 (2006), no. 5, 351–362.[MR]
  70. Ilias S. Kotsireas, Christos Koukouvinos, and Jennifer Seberry, Hadamard ideals and Hadamard matrices with circulant core, J. Combin. Math. Combin. Comput. 57 (2006), 47–63.[MR]
  71. Ilias S. Kotsireas, Christos Koukouvinos, and Jennifer Seberry, Hadamard ideals and Hadamard matrices with two circulant cores, European J. Combin. 27 (2006), no. 5, 658–668.[MR]
  72. C. Koukouvinos and S. Stylianou, On skew-Hadamard matrices, Discrete Math. 308 (2008), no. 13, 2723–2731.[MR]
  73. Christos Koukouvinos and Dimitris E. Simos, Improving the lower bounds on inequivalent Hadamard matrices through orthogonal designs and meta-programming techniques, Applied Numerical Mathematics, to appear (2009).
  74. Warwick de Launey and Richard M. Stafford, On cocyclic weighing matrices and the regular group actions of certain Paley matrices, Discrete Appl. Math. 102 (2000), no. 1-2, 63–101.[MR]
  75. Wolfgang Lempken, Two new symmetric 2-(144,66,30) designs, Preprint.
  76. Keith E. Mellinger, Designs, Geometry, and a Golfer's Dilemma, Math. Mag. 77 (2004), no. 4, 275–282.[MR]
  77. Jamshid Moori and B. G. Rodrigues, Some designs and codes invariant under the simple group Co2, J. Algebra 316 (2007), no. 2, 649–661.[MR]
  78. Akihiro Munemasa and Vladimir D. Tonchev, A new quasi-symmetric 2-(56,16,6) design obtained from codes, Discrete Math. 284 (2004), no. 1-3, 231–234.[MR]
  79. Werner Nickel, Alice C. Niemeyer, Christine M. O'Keefe, Tim Penttila, and Cheryl E. Praeger, The block-transitive, point-imprimitive 2-(729,8,1) designs, Appl. Algebra Engrg. Comm. Comput. 3 (1992), no. 1, 47–61.[MR]
  80. Christopher Parker, Edward Spence, and Vladimir D. Tonchev, Designs with the symmetric difference property on 64 points and their groups, J. Combin. Theory Ser. A 67 (1994), no. 1, 23–43.[MR]
  81. Christopher Parker and Vladimir D. Tonchev, Linear codes and doubly transitive symmetric designs, Linear Algebra Appl. 226/228 (1995), 237–246.[MR]
  82. E. M. Rains, N. J. A. Sloane, and John Stufken, The lattice of N-run orthogonal arrays, J. Statist. Plann. Inference 102 (2002), no. 2, 477–500.[MR]
  83. Colin Ramsay, Trades and defining sets: theoretical and computational results, PhD Thesis, University of Queensland, 1998.
  84. B. G. Rodrigues, Self-orthogonal designs and codes from the symplectic groups S4(3) and S4(4), Discrete Math. 308 (2008), no. 10, 1941–1950.[MR]
  85. Nagwa Kamal Ahmed Rostom, On the p-rank of t-designs, Master's Thesis, University of Birmingham, 1985.
  86. Chekad Sarami and Vladimir D. Tonchev, Cyclic quasi-symmetric designs and self-orthogonal codes of length 63, J. Statist. Plann. Inference 138 (2008), no. 1, 80–85.[MR]
  87. Bernd Schmalz, t-Designs zu vorgegebener Automorphismengruppe, Bayreuth. Math. Schr. (1992), no. 41, 164.[MR]
  88. Michel Sebille, On a result of Cameron and Praeger on block-transitive point-imprimitive t-designs, Algebraic Combinatorics and Applications (Gößweinstein, 1999), Springer, Berlin, 2001, pp. 316–323.[MR]
  89. Martin J. Sharry, Partitioning sets of quintuples into designs, J. Combin. Math. Combin. Comput. 6 (1989), 67–103.[MR]
  90. Junichi Shigezumi, On 3-lattices and spherical designs, preprint (2008), 199 pages.[arXiv]
  91. Pawel Wocjan, Efficient decoupling schemes with bounded controls based on Eulerian orthogonal arrays, Phy. Rev. A. 73 (2006), no. 6, 7.