Cyclic codes over {Z2+uZ2+u2Z2+\ldots+uk-1Z2}

In this paper, we study the structure of cyclic codes of an arbitrary length n over the ring Z2+uZ2+u2Z2+\ldots+uk-1Z2, where uk=0. Also we study the rank for these codes, and we find their minimal spanning sets. This study is a generalization and extension of the work in reference [1].

Anahtar Kelimeler:

Cyclic codes, Codes over rings, Hamming weight

Cyclic codes over {Z2+uZ2+u2Z2+\ldots+uk-1Z2}

Keywords:

Cyclic codes, Codes over rings, Hamming weight,

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and Z2 , Designs Codes and Cryptography. Vol.42, No.3, 273-287(2007).
Abualrub, T. and Oehmke, R.: On the generators of Z cyclic codes, IEEE Trans. Inform. Theory. Vol.49, No.9, 2133(2003).
Blackford, T.: Cyclic codes over Z4of oddly even length, Discrete Applied Mathematics. Vol.128, 27-46(2003).
Bonnecaze, A. and Udaya, P.: Cyclic codes and self-dual codes over F2+ uF, IEEE Trans. Inform. Theory. Vol.45, No.4, 1250-1255(1999).
Calderbank, A., Rains, E., Shor, P., Neil, J. and Sloane, N.J.A.: Quantum error corrections via codes over GF(4), IEEE Transactions on Information Theory. Vol.4, No.4, 1369-1387(1998).
Calderbank, A. and Sloane, N.J.A.: Modular and P-adic cyclic codes, Des. Codes Crypt. Vol.37, No.6, 21-35(1995).
Dinh, H. and Lopez-Permouth, S.: Cyclic and negacyclic codes over Şnite chain rings, IEEE Trans. Inform. Theory. Vol.50, No.8, 1728-1744(2004).
Dougherty, ST. and Shiromoto, K.: Maximum distance codes over rings of order 4, IEEE Trans. Inform. Theory. Vol.47, No.1, 400-404 (2001).
Noton, G. and Salagean, A.: On the structure of linear and cyclic codes over a Şnite chain ring, Applicable Algebra Engineering Communication and Computing. Vol.10, No.6, 489-506 (2000).
Pless, V. and Qian, Z.: Cyclic codes and quadratic residue codes over Z, IEEE Trans. Inform. Theory. Vol.45, No.5, 1594-1600 (1996).
Van Lint, J.: Repeated-root cyclic codes, IEEE Trans. Inform. Theory. Vol.37, No.2, 343-345(1977). Mohammed AL-ASHKER
Department of Mathematics, Islamic University of Gaza-PALESTINE e-mail: mashker@iugaza.edu.ps Mohammed HAMOUDEH Ministry of education, Gaza-PALESTINE e-mail: mamh 73@hotmail.com