Mass Formula of Self-dual codes over Galois rings $GR(p^2,2)$
Main Article Content
Abstract
Article Details
References
[1] Jose Maria P. Balmaceda, Rowena Alma L. Betty, and Fidel R. Nemenzo, Mass formula for self-dual codes over Zp2 , Discrete Mathematics 308 (14) (2008), 2984–3002. Google Scholar
[2] A. R. Calderbank and N. J. A. Sloane, Modular and p-adic cyclic codes, Des. Codes Cryptography, 6 (1) (1995), 21–35. Google Scholar
[3] Whan-Hyuk Choi, Kwang Ho Kim, and Sook Young Park, The classification of self-orthogonal codes over Zp2 of length ≤ 3, Korean Journal of Mathematics 22 (4) (2014), 725–742. Google Scholar
[4] Philippe Gaborit, Mass formulas for self-dual codes over Z4 and Fq +uFq rings, Information Theory IEEE Transactions on 42 (4) (1996) 1222–1228. Google Scholar
[5] Fernando Q. Gouvˆea, p-adic Numbers, Springer, 1997. Google Scholar
[6] Roger A. Hammons, Vijay P. Kumar, A. Robert Calderbank, N. Sloane, and Patrick Sol´e, The Z4-linearity of Kerdock, Preparata, Goethals, and related codes, Information Theory IEEE Transactions on 40 (2) (1994), 301–319. Google Scholar
[7] Jon-Lark Kim and Yoonjin Lee, Construction of MDS self-dual codes over Galois rings, Designs, Codes and Cryptography, 45 (2) (2007), 247–258. Google Scholar
[8] Rudolf Lidl and Harald Niederreiter, Finite fields: Encyclopedia of mathematics and its applications, Computers & Mathematics with Applications 33 (7) (1997), 136–136. Google Scholar
[9] Bernard R. McDonald, Finite rings with identity, volume 28. Marcel Dekker Incorporated, 1974. Google Scholar
[10] Kiyoshi Nagata, Fidel Nemenzo, and Hideo Wada, Constructive algorithm of self-dual error-correcting codes In Proc. of 11th International Workshop on Algebraic and Combinatorial Coding Theory, pages 215–220, 2008. Google Scholar
[11] Kiyoshi Nagata, Fidel Nemenzo, and Hideo Wada, The number of self-dual codes over Zp3 , Designs, Codes and Cryptography 50 (3) (2009), 291–303. Google Scholar
[12] Kiyoshi Nagata, Fidel Nemenzo, and Hideo Wada, Mass formula and structure of self-dual codes over Z2 s , Designs, codes and cryptography 67 (3) (2013), 293–316. Google Scholar
[13] Young Ho Park, The classification of self-dual modular codes, Finite Fields and Their Applications 17 (5) (2011), 442–460. Google Scholar
[14] Vera Pless, The number of isotropic subspaces in a finite geometry Atti. Accad. Naz. Lincei Rendic 39 (1965), 418–421. Google Scholar
[15] Vera Pless, On the uniqueness of the golay codes, Journal of Combinatorial theory 5 (3) (1968), 215–228. Google Scholar
[16] Zhe-Xian Wan, Finite Fields And Galois Rings, World Scientific Publishing Co., Inc., 2011. Google Scholar