On ?2?2[u]-additive codes |
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Authors: | Ismail Aydogdu Taher Abualrub Irfan Siap |
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Affiliation: | 1. Department of Mathematics, Yildiz Technical University, Istanbul, Turkeyiaydogdu@yildiz.edu.trismayilaydogdu@windowslive.com;4. Department of Mathematics and Statistics, American University of Sharjah, Sharjah, United Arab Emirates;5. Department of Mathematics, Yildiz Technical University, Istanbul, Turkey |
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Abstract: | In this paper, a new class of additive codes which is referred to as ?2 ?2u]-additive codes is introduced. This is a generalization towards another direction of recently introduced ?2 ?4-additive codes J. Borges, C. Fernández-Córdoba, J. Pujol, J. Rif´a, and M. Villanueva, ?2 ?4-linear codes: Generator matrices and duality, Designs Codes Cryptogr. 54(2) (2010), pp. 167–179]. ?2 ?4-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 ?2 ?2u]-additive codes are presented. |
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Keywords: | ?2?2[u]-additive codes generator matrix parity-check matrix MacWilliams identity |
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