Coding Theory

Codes over Galois Rings

  1. Nuh Aydin, Tsvetan Asamov, and T. Aaron Gulliver, Some open problems on quasi-twisted and related code constructions and good quaternary codes, IEEE International Symposium on Information Theory, 2007. ISIT 2007 (2007), 856-860.[doi]
  2. Christine Bachoc, T. Aaron Gulliver, and Masaaki Harada, Isodual codes over Z2k and isodual lattices, J. Algebraic Combin. 12 (2000), no. 3, 223–240.[MR]
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  4. Delphine Boucher, Patrick Solé, and Felix Ulmer, Skew constacyclic codes over Galois rings, Adv. Math. Commun. 2 (2008), no. 3, 273–292.[MR]
  5. Eimear Byrne, Marcus Greferath, and Michael E. O'Sullivan, The linear programming bound for codes over finite Frobenius rings, Des. Codes Cryptogr. 42 (2007), no. 3, 289–301.[MR]
  6. A. R. Calderbank and N. J. A. Sloane, Double circulant codes over Z4 and even unimodular lattices, J. Algebraic Combin. 6 (1997), no. 2, 119–131.[MR]
  7. Marcus Greferath and Emanuele Viterbo, On Z4- and Z9-linear lifts of the Golay codes, IEEE Trans. Inform. Theory 45 (1999), no. 7, 2524–2527.[MR]
  8. T. Aaron Gulliver and Masaaki Harada, Optimal double circulant Z4-codes, Applied Algebra, Algebraic Algorithms and Error-correcting Codes (Melbourne, 2001), Lecture Notes in Comput. Sci., vol. 2227, Springer, Berlin, 2001, pp. 122–128.[MR]
  9. T. Aaron Gulliver, Patric R. J. Östergård, and Nikolai I. Senkevitch, Optimal quaternary linear rate-1/2 codes of length ≤ 18, IEEE Trans. Inform. Theory 49 (2003), no. 6, 1540–1543.[MR/link]
  10. Masaaki Harada, Extremal type II Z4-codes of lengths 56 and 64, J. Combin. Theory Ser. A 117 (2010), no. 8, 1285–1288.[MR/doi]
  11. Masaaki Harada and Tsuyoshi Miezaki, An upper bound on the minimum weight of type ii-codes, J Combin. Theory Ser. A 118 (2010), no. 1, 190–196.[doi]
  12. M. Kiermaier and A. Wassermann, On the minimum Lee distance of quadratic residue codes over Z4, IEEE International Symposium on Information Theory, 2008. ISIT 2008. (2008), 2617-2619.[doi]
  13. Jon-Lark Kim and Yoonjin Lee, Construction of MDS self-dual codes over Galois rings, Des. Codes Cryptogr. 45 (2007), no. 2, 247–258.[MR]
  14. J. Pernas, J. Pujol, and M. Villanueva, Kernel dimension for some families of quaternary Reed-Muller codes, Information Security, Lecture Notes in Comput. Sci., vol. 5393, Springer, Berlin, 2008, pp. 128–141.
  15. Patrick Solé and Virgilio Sison, Bounds on the minimum homogeneous distance of the p-ary image of linear block codes over the Galois ring GR(pr,m), IEEE Trans. Inform. Theory 53 (2007), no. 6, 2270–2273.[MR]