Mass Formula of Self-dual codes over Galois rings $GR(p^2,2)$

Whanhyuk Choi

Abstract


We investigate the self-dual codes over Galois rings and determine the mass formula for self-dual codes over Galois rings $GR(p^2,2)$.

Keywords


codes over Galois ring, self-dual codes, mass formula

Full Text:

PDF

References


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.

A. R. Calderbank and N. J. A. Sloane, Modular and p-adic cyclic codes, Des. Codes Cryptography, 6 (1) (1995), 21–35.

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.

Philippe Gaborit, Mass formulas for self-dual codes over Z4 and Fq +uFq rings, Information Theory IEEE Transactions on 42 (4) (1996) 1222–1228.

Fernando Q. Gouvˆea, p-adic Numbers, Springer, 1997.

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.

Jon-Lark Kim and Yoonjin Lee, Construction of MDS self-dual codes over Galois rings, Designs, Codes and Cryptography, 45 (2) (2007), 247–258.

Rudolf Lidl and Harald Niederreiter, Finite fields: Encyclopedia of mathematics and its applications, Computers & Mathematics with Applications 33 (7) (1997), 136–136.

Bernard R. McDonald, Finite rings with identity, volume 28. Marcel Dekker Incorporated, 1974.

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.

Kiyoshi Nagata, Fidel Nemenzo, and Hideo Wada, The number of self-dual codes over Zp3 , Designs, Codes and Cryptography 50 (3) (2009), 291–303.

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.

Young Ho Park, The classification of self-dual modular codes, Finite Fields and Their Applications 17 (5) (2011), 442–460.

Vera Pless, The number of isotropic subspaces in a finite geometry Atti. Accad. Naz. Lincei Rendic 39 (1965), 418–421.

Vera Pless, On the uniqueness of the golay codes, Journal of Combinatorial theory 5 (3) (1968), 215–228.

Zhe-Xian Wan, Finite Fields And Galois Rings, World Scientific Publishing Co., Inc., 2011.




DOI: http://dx.doi.org/10.11568/kjm.2016.24.4.751

Refbacks

  • There are currently no refbacks.


ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr