1. On ℤ 2 ℤ 2 [ u ]-additive codes.
- Author
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Aydogdu, Ismail, Abualrub, Taher, and Siap, Irfan
- Subjects
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ADDITION (Mathematics) , *CODING theory , *SET theory , *DUALITY theory (Mathematics) , *ORDERED algebraic structures - Abstract
In this paper, a new class of additive codes which is referred to as ℤ2ℤ2[u]-additive codes is introduced. This is a generalization towards another direction of recently introduced ℤ2ℤ4-additive codes [J. Borges, C. Fernández-Córdoba, J. Pujol, J. Rif´a, and M. Villanueva, ℤ2ℤ4-linear codes: Generator matrices and duality, Designs Codes Cryptogr. 54(2) (2010), pp. 167–179]. ℤ2ℤ4-additive codes have shown to provide a promising class of codes with their algebraic structure and applications such as steganography. The standard generator matrices are established and by introducing orthogonality the parity-check matrices are also obtained. A MacWilliams-type identity that relates the weight enumerator of a code with its dual is proved. Furthermore, a Gray map that maps these codes to binary codes is defined and some examples of optimal codes which are the binary Gray images of ℤ2ℤ2[u]-additive codes are presented. [ABSTRACT FROM PUBLISHER]
- Published
- 2015
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