Coding Theory

Combinatorial Codes

94B25

  1. 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]
  2. E. F. Assmus, Jr., The coding theory of finite geometries and designs, Applied Algebra, Algebraic Algorithms and Error-correcting Codes (Rome, 1988), Lecture Notes in Comput. Sci., vol. 357, Springer, Berlin, 1989, pp. 1–6.[MR]
  3. E. F. Assmus, Jr. and Arthur A. Drisko, Binary codes of odd-order nets, Des. Codes Cryptogr. 17 (1999), no. 1-3, 15–36.[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. E. F. Assmus, Jr. and J. D. Key, Designs and codes: an update, Des. Codes Cryptogr. 9 (1996), no. 1, 7–27.[MR]
  6. E. F. Assmus, Jr. and J. D. Key, Polynomial codes and finite geometries, Handbook of Coding Theory, Vol. I, II, North-Holland, Amsterdam, 1998, pp. 1269–1343.[MR]
  7. Robert F. Bailey and John N. Bray, Decoding the Mathieu group M12, Adv. Math. Commun. 1 (2007), no. 4, 477–487.[MR]
  8. R. D. Baker and K. L. Wantz, Unitals in the code of the Hughes plane, J. Combin. Des. 12 (2004), no. 1, 35–38.[MR]
  9. Koichi Betsumiya, T. Aaron Gulliver, Masaaki Harada, and Akihiro Munemasa, On type II codes over F4, IEEE Trans. Inform. Theory 47 (2001), no. 6, 2242–2248.[MR]
  10. Neil J. Calkin, Jennifer D. Key, and Marialuisa J. de Resmini, Minimum weight and dimension formulas for some geometric codes, Des. Codes Cryptogr. 17 (1999), no. 1-3, 105–120.[MR]
  11. L. L. Carpenter and J. D. Key, Reed-Muller codes and Hadamard designs from ovals, J. Combin. Math. Combin. Comput. 22 (1996), 79–85.[MR]
  12. Ying Cheng and N. J. A. Sloane, Codes from symmetry groups, and a [32,17,8] code, SIAM J. Discrete Math. 2 (1989), no. 1, 28–37.[MR]
  13. Naoki Chigira, Masaaki Harada, and Masaaki Kitazume, Permutation groups and binary self-orthogonal codes, J. Algebra 309 (2007), no. 2, 610–621.[MR]
  14. Naoki Chigira, Masaaki Harada, and Masaaki Kitazume, Some self-dual codes invariant under the Hall-Janko group, J. Algebra 316 (2007), no. 2, 578–590.[MR]
  15. K. L. Clark, J. D. Key, and M. J. de Resmini, Dual codes of translation planes, European J. Combin. 23 (2002), no. 5, 529–538.[MR]
  16. Marston Conder and John McKay, Markings of the Golay code, New Zealand J. Math. 25 (1996), no. 2, 133–139.[MR]
  17. A. Cossidente and A. Sonnino, A geometric construction of a [110,5,90]9-linear code admitting the Mathieu group M11, IEEE Trans. Inform. Theory 54 (2008), no. 11, 5251-5252.[doi]
  18. Antonio Cossidente and Alessandro Siciliano, A geometric construction of an optimal [67,9,30] binary code, IEEE Trans. Inform. Theory 47 (2001), no. 3, 1187–1189.[MR]
  19. 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]
  20. M. van Dijk, S. Egner, M. Greferath, and A. Wassermann, Geometric codes over fields of odd prime power order, in IEEE International Symposium on Information Theory (ISIT), Yokohama, 2003.
  21. Steven T. Dougherty, Jon-Lark Kim, and Patrick Solé, Double circulant codes from two class association schemes, Adv. Math. Commun. 1 (2007), no. 1, 45–64.[MR]
  22. Sean V. Droms, Keith E. Mellinger, and Chris Meyer, LDPC codes generated by conics in the classical projective plane, Des. Codes Cryptogr. 40 (2006), no. 3, 343–356.[MR]
  23. D. G. Farmer and K. J. Horadam, Presemifield bundles over GF(p3), IEEE International Symposium on Information Theory, 2008. ISIT 2008 (2008), 2613-2616.[doi]
  24. 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]
  25. W. Fish, J. D. Key, and E. Mwambene, Binary codes from the line graph of the n-cube, J. Symbolic Comput. 45 (2010), no. 7, 800–812.[MR/doi]
  26. W. Fish, J. D. Key, and E. Mwambene, Codes from incidence matrices and line graphs of Hamming graphs, Discrete Math. 310 (2010), no. 13-14, 1884–1897.[MR/doi]
  27. S. Gao and J. D. Key, Bases of minimum-weight vectors for codes from designs, Finite Fields Appl. 4 (1998), no. 1, 1–15.[MR]
  28. D. Ghinelli, M. J. de Resmini, and J. D. Key, Minimum words of codes from affine planes, J. Geom. 91 (2009), no. 1-2, 43–51.
  29. Markus Grassl and T. Aaron Gulliver, On circulant self-dual codes over small fields, Des. Codes Cryptogr. 52 (2009), no. 1, 57–81.[MR]
  30. Willem H. Haemers, Christopher Parker, Vera Pless, and Vladimir Tonchev, A design and a code invariant under the simple group Co3, J. Combin. Theory Ser. A 62 (1993), no. 2, 225–233.[MR]
  31. 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]
  32. 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]
  33. K. J. Horadam and P. Udaya, A new class of ternary cocyclic Hadamard codes, Appl. Algebra Engrg. Comm. Comput. 14 (2003), no. 1, 65–73.[MR]
  34. J. D. Key, Bases for codes of designs from finite geometries, in Proceedings of the Twenty-fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1994), vol. 102, 1994, pp. 33–44.[MR]
  35. J. D. Key, Some applications of Magma in designs and codes: Oval designs, Hermitian unitals and generalized Reed-Muller codes, J. Symbolic Comput. 31 (2001), no. 1-2, 37–53.[MR]
  36. J. D. Key, Recent developments in permutation decoding, Not. S. Afr. Math. Soc. 37 (2006), no. 1, 2–13.[MR]
  37. J. D. Key, T. P. McDonough, and V. C. Mavron, Information sets and partial permutation decoding for codes from finite geometries, Finite Fields Appl. 12 (2006), no. 2, 232–247.[MR]
  38. J. D. Key, T. P. McDonough, and V. C. Mavron, Partial permutation decoding for codes from affine geometry designs, J. Geom. 88 (2008), no. 1-2, 101–109.[MR]
  39. J. D. Key and J. Moori, Some irreducible codes invariant under the Janko group, J1 or J2, preprint (2008), 20 pages.
  40. J. D. Key, J. Moori, and B. G. Rodrigues, On some designs and codes from primitive representations of some finite simple groups, J. Combin. Math. Combin. Comput. 45 (2003), 3–19.[MR]
  41. J. D. Key, J. Moori, and B. G. Rodrigues, Binary codes from graphs on triples, Discrete Math. 282 (2004), no. 1-3, 171–182.[MR]
  42. J. D. Key, J. Moori, and B. G. Rodrigues, Permutation decoding for the binary codes from triangular graphs, European J. Combin. 25 (2004), no. 1, 113–123.[MR]
  43. J. D. Key, J. Moori, and B. G. Rodrigues, Some binary codes from symplectic geometry of odd characteristic, Util. Math. 67 (2005), 121–128.[MR]
  44. J. D. Key, J. Moori, and B. G. Rodrigues, Partial permutation decoding of some binary codes from graphs on triples, Ars Combin. 91 (2009), 363–371.[MR]
  45. J. D. Key, J. Moori, and B. G. Rodrigues, Ternary codes from graphs on triples, Discrete Math. 309 (2009), no. 14, 4663–4681.[MR/doi]
  46. J. D. Key, J. Moori, and B. G. Rodrigues, Codes associated with triangular graphs, and permutation decoding, International Journal of Information and Coding Theory 1 (2010), no. 3, 334–349 pages.
  47. 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]
  48. J. D. Key and M. J. de Resmini, Ternary dual codes of the planes of order nine, J. Statist. Plann. Inference 95 (2001), no. 1-2, 229–236.[MR]
  49. J. D. Key and P. Seneviratne, Permutation decoding for binary codes from lattice graphs, Discrete Math. 308 (2008), no. 13, 2862–2867.[MR]
  50. Jon-Lark Kim and Vera Pless, Designs in additive codes over GF(4), Des. Codes Cryptogr. 30 (2003), no. 2, 187–199.[MR]
  51. Jon-Lark Kim and Patrick Solé, Skew Hadamard designs and their codes, Des. Codes Cryptogr. 49 (2008), no. 1-3, 135–145.[MR]
  52. Heisook Lee and Yoonjin Lee, Construction of self-dual codes over finite rings Zpm, J. Combin. Theory Ser. A 115 (2008), no. 3, 407–422.[MR]
  53. Ka Hin Leung and Qing Xiang, On the dimensions of the binary codes of a class of unitals, Discrete Math. 309 (2009), no. 3, 570–575.[MR/doi]
  54. San Ling and Chaoping Xing, Polyadic codes revisited, IEEE Trans. Inform. Theory 50 (2004), no. 1, 200–207.[MR]
  55. Kirsten Mackenzie, Codes of designs, PhD Thesis, University of Birmingham, 1989.
  56. Johannes Maks and Juriaan Simonis, Optimal subcodes of second order Reed-Muller codes and maximal linear spaces of bivectors of maximal rank, Des. Codes Cryptogr. 21 (2000), no. 1-3, 165–180.[MR]
  57. Stefano Marcugini, Alfredo Milani, and Fernanda Pambianco, NMDS codes of maximal length over Fq, 8 ≤ q ≤ 11, IEEE Trans. Inform. Theory 48 (2002), no. 4, 963–966.[MR]
  58. Stefano Marcugini, Alfredo Milani, and Fernanda Pambianco, Classification of the (n,3)-arcs in PG(2,7), J. Geom. 80 (2004), no. 1-2, 179–184.[MR]
  59. Gary McGuire and Harold N. Ward, A determination of the weight enumerator of the code of the projective plane of order 5, Note Mat. 18 (1998), no. 1, 71–99 (1999).[MR]
  60. Gary McGuire and Harold N. Ward, The weight enumerator of the code of the projective plane of order 5, Geom. Dedicata 73 (1998), no. 1, 63–77.[MR]
  61. 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]
  62. 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]
  63. Mona B. Musa, On some double circulant binary extended quadratic residue codes, IEEE Trans. Inform. Theory 54 (2008), no. 2, 898–905.[MR]
  64. Christopher Parker and Vladimir D. Tonchev, Linear codes and doubly transitive symmetric designs, Linear Algebra Appl. 226/228 (1995), 237–246.[MR]
  65. Steven R. Weller and Sarah J. Johnson, Iterative decoding of codes from oval designs, Defence Applications of Signal Processing, 2001 Workshop (2001), 1-19.