Coding Theory

Linear Codes: General

94B05, 94B12, 94B60

  1. Salah A. Aly, Asymmetric and symmetric subsystem BCH codes and beyond, preprint (2008), 10 pages.[arXiv]
  2. E. F. Assmus, Jr. and J. D. Key, Designs and codes: an update, Des. Codes Cryptogr. 9 (1996), no. 1, 7–27.[MR]
  3. 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]
  4. Christine Bachoc, On harmonic weight enumerators of binary codes, Des. Codes Cryptogr. 18 (1999), no. 1-3, 11–28.[MR]
  5. Christine Bachoc, Harmonic weight enumerators of nonbinary codes and MacWilliams identities, Codes and Association Schemes (Piscataway, NJ, 1999), DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 56, Amer. Math. Soc., Providence, RI, 2001, pp. 1–23.[MR]
  6. Lynn M. Batten, Michelle Davidson, and Leo Storme, An analysis of Chen's construction of minimum-distance five codes, IEEE Trans. Inform. Theory 46 (2000), no. 2, 505–511.[MR]
  7. Thierry P. Berger, Goppa and related codes invariant under a prescribed permutation, IEEE Trans. Inform. Theory 46 (2000), no. 7, 2628–2633.[MR]
  8. Koichi Betsumiya, T. Aaron Gulliver, and Masaaki Harada, Binary optimal linear rate 1/2 codes, Applied Algebra, Algebraic Algorithms and Error-correcting Codes (Honolulu, HI, 1999), Lecture Notes in Comput. Sci., vol. 1719, Springer, Berlin, 1999, pp. 462–471.[MR]
  9. Ezio Biglieri, John K. Karlof, and Emanuele Viterbo, Representing group codes as permutation codes, IEEE Trans. Inform. Theory 45 (1999), no. 6, 2204–2207.[MR]
  10. Delphine Boucher and Felix Ulmer, Coding with skew polynomial rings, J. Symbolic Comput. 44 (2009), no. 12, 1644–1656.[MR/doi]
  11. Iliya Bouyukliev and Valentin Bakoev, A method for efficiently computing the number of codewords of fixed weights in linear codes, Discrete Appl. Math. 156 (2008), no. 15, 2986–3004.[MR]
  12. Iliya Bouyukliev, Markus Grassl, and Zlatko Varbanov, New bounds for n4(k,d) and classification of some optimal codes over GF(4), Discrete Math. 281 (2004), no. 1-3, 43–66.[MR]
  13. Iliya Bouyukliev and Juriaan Simonis, Some new results for optimal ternary linear codes, IEEE Trans. Inform. Theory 48 (2002), no. 4, 981–985.[MR]
  14. Thomas Britz and Keisuke Shiromoto, Designs from subcode supports of linear codes, Des. Codes Cryptogr. 46 (2008), no. 2, 175–189.[MR]
  15. Stanislav Bulygin and Ruud Pellikaan, Bounded distance decoding of linear error-correcting codes with Gröbner bases, J. Symb. Comput. 44 (2009), no. 12, 1626–1643.
  16. A. Robert Calderbank, Eric M. Rains, P. W. Shor, and Neil J. A. Sloane, Quantum error correction via codes over GF(4), IEEE Trans. Inform. Theory 44 (1998), no. 4, 1369–1387.[MR]
  17. Lionel Chaussade, Pierre Loidreau, and Felix Ulmer, Skew codes of prescribed distance or rank, Des. Codes Cryptogr. Online first (2008), 18.
  18. Anne Desideri Bracco, Treillis de codes quasi-cycliques, European J. Combin. 25 (2004), no. 4, 505–516.[MR]
  19. M. van Dijk, S. Egner, M. Greferath, and A. Wassermann, On binary linear [160,80,24] codes, in IEEE International Symposium on Information Theory (ISIT), Yokohama, 2003.
  20. Cunsheng Ding, David Kohel, and San Ling, Elementary 2-group character codes, IEEE Trans. Inform. Theory 46 (2000), no. 1, 280–284.[MR]
  21. Peng Ding and Jennifer D. Key, Minimum-weight codewords as generators of generalized Reed-Muller codes, IEEE Trans. Inform. Theory 46 (2000), no. 6, 2152–2158.[MR]
  22. Peng Ding and Jennifer D. Key, Subcodes of the projective generalized Reed-Muller codes spanned by minimum-weight vectors, Des. Codes Cryptogr. 26 (2002), no. 1-3, 197–211.[MR]
  23. M. van Eupen and P. Lisonek, Classification of some optimal ternary linear codes of small length, Designs, Codes and Cryptography 10 (1997), 63–84.
  24. Thomas Feulner, The automorphism groups of linear codes and canonical representatives of their semilinear isometry classes, Adv. Math. Commun. 3 (2009), no. 4, 363–383.[MR/doi]
  25. Luís R. A. Finotti, Minimal degree liftings in characteristic 2, J. Pure Appl. Algebra 207 (2006), no. 3, 631–673.[MR]
  26. Philippe Gaborit, Quadratic double circulant codes over fields, J. Combin. Theory Ser. A 97 (2002), no. 1, 85–107.[MR]
  27. Philippe Gaborit, W. Cary Huffman, Jon-Lark Kim, and Vera Pless, On additive GF(4) codes, Codes and Association Schemes (Piscataway, NJ, 1999), DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 56, Amer. Math. Soc., Providence, RI, 2001, pp. 135–149.[MR]
  28. Philippe Gaborit and Oliver D. King, Linear constructions for DNA codes, Theoret. Comput. Sci. 334 (2005), no. 1-3, 99–113.[MR]
  29. Philippe Gaborit, Carmen-Simona Nedeloaia, and Alfred Wassermann, Weight enumerators of duadic and quadratic residue codes, in IEEE International Symposium on Information Theory (ISIT), Chicago, USA, 2004.
  30. Julia Galstad and Gerald Hoehn, A new class of codes over Z2×Z2, preprint (2010), 29 pages.[arXiv]
  31. Santos González, Consuelo Martínez, and Alejandro P. Nicolás, Classic and quantum error correcting codes, Coding Theory and Applications, Lecture Notes in Computer Science, vol. 5228, Springer, 2008, pp. 56-68.
  32. Daniel M. Gordon, Victor Miller, and Peter Ostapenko, Optimal hash functions for approximate closest pairs on the n-cube, preprint (2008).[arXiv]
  33. M. Grassl and G. White, New good linear codes by special puncturings, International Symposium on Information Theory, 2004. ISIT 2004 (2004), 454-.
  34. Fernando Hernando and Diego Ruano, Sixteen new linear codes with Plotkin sum, preprint (2008), 2 pages.[arXiv]
  35. W. Cary Huffman and Vera Pless, Fundamentals of Error-correcting Codes, Cambridge University Press, Cambridge, 2003, pp. xviii+646.[MR]
  36. Paul Hurley and Ted Hurley, Codes from zero-divisors and units in group rings, International Journal of Information and Coding Theory 1 (2009), no. 1, 57–87.[arXiv]
  37. Ted Hurley, Convolutional codes from units in matrix and group rings, Int. J. Pure Appl. Math. 50 (2009), no. 3, 431–463.[MR/arXiv]
  38. Martin Janošov, Martin Husák, Peter Farkaš, and Ana Garcia Armada, New [47,15,16] linear binary block code, IEEE Trans. Inform. Theory 54 (2008), no. 1, 423–424.[MR]
  39. John K. Karlof and Yaw O. Chang, Optimal permutation codes for the Gaussian channel, IEEE Trans. Inform. Theory 43 (1997), no. 1, 356–358.[MR]
  40. J. D. Key, Codes and finite geometries, in Proceedings of the Twenty-ninth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1998), vol. 131, 1998, pp. 85–99.[MR]
  41. J. D. Key, Some error-correcting codes and their applications, Applied Mathematical Modeling: A Multidisciplinary Approach, Edited by D. R. Shier and K. T. Wallenius, CRC Press, Boca Raton, Fl., 1999.
  42. J. D. Key, B. Novick, and F. E. Sullivan, Binary codes of structures dual to unitals, in Proceedings of the Twenty-eighth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1997), vol. 123, 1997, pp. 119–124.[MR]
  43. J. D. Key and P. Seneviratne, Binary codes from rectangular lattice graphs and permutation decoding, European J. Combin. 28 (2007), no. 1, 121–126.[MR]
  44. Dae San Kim, Codes associated with O+(2n,2r) and power moments of Kloosterman sums, preprint (2008), 9 pages.[arXiv]
  45. Dae San Kim, Codes associated with orthogonal groups and power moments of Kloosterman sums, preprint (2008).[arXiv]
  46. Dae San Kim, Codes associated with special linear groups and power moments of multi-dimensional Kloosterman sums, preprint (2008), 7 pages.[arXiv]
  47. Jon-Lark Kim, Keith E. Mellinger, and Vera Pless, Projections of binary linear codes onto larger fields, SIAM J. Discrete Math. 16 (2003), no. 4, 591–603 (electronic).[MR]
  48. Chong Jie Lim, Consta-abelian polyadic codes, IEEE Trans. Inform. Theory 51 (2005), no. 6, 2198–2206.[MR]
  49. San Ling, Chaoping Xing, and Ferruh Özbudak, An explicit class of codes with good parameters and their duals, Discrete Appl. Math. 154 (2006), no. 2, 346–356.[MR]
  50. J. Löfvenberg, Binary fingerprinting codes, Des. Codes Cryptogr. 36 (2005), no. 1, 69–81.[MR]
  51. Stefano Marcugini, Alfredo Milani, and Fernanda Pambianco, Classification of linear codes exploiting an invariant, Contrib. Discrete Math. 1 (2006), no. 1, 1–7 (electronic).[MR]
  52. Patric R. J. Östergård, Classifying subspaces of Hamming spaces, Des. Codes Cryptogr. 27 (2002), no. 3, 297–305.[MR]
  53. Kevin T. Phelps, An enumeration of 1-perfect binary codes, Australas. J. Combin. 21 (2000), 287–298.[MR]
  54. Ralph-Hardo Schulz, Check character systems and anti-symmetric mappings, Computational Discrete Mathematics, Lecture Notes in Comput. Sci., vol. 2122, Springer, Berlin, 2001, pp. 136–147.[MR]
  55. Anuradha Sharma, Gurmeet K. Bakshi, and Madhu Raka, Polyadic codes of prime power length, Finite Fields Appl. 13 (2007), no. 4, 1071–1085.[MR]
  56. Derek H. Smith, Niema Aboluion, Roberto Montemanni, and Stephanie Perkins, Linear and nonlinear constructions of DNA codes with Hamming distance d and constant GC-content, Discrete Math., to appear (2010).[doi]
  57. C. Tjhai, M. Tomlinson, M. Grassl, R. Horan, M. Ahmed, and M. Ambroze, New linear codes derived from binary cyclic codes of length 151, IEE Proceedings: Communications 153 (2006), no. 5, 581–585.
  58. Judy L. Walker, Constructing critical indecomposable codes, IEEE Trans. Inform. Theory 47 (2001), no. 5, 1780–1795.[MR]
  59. Harold N. Ward, An Introduction to Algebraic Coding Theory, Coding Theory and Quantum Computing, Contemp. Math., vol. 381, Amer. Math. Soc., Providence, RI, 2005, pp. 27–52.[MR]