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Construction of MDS self-dual codes over Galois rings
- Construction of MDS self-dual codes over Galois rings
- Kim J.-L.; Lee Y.
- Ewha Authors
- SCOPUS Author ID
- Issue Date
- Journal Title
- Designs, Codes, and Cryptography
- vol. 45, no. 2, pp. 247 - 258
- SCI; SCIE; SCOPUS
- The purpose of this paper is to construct nontrivial MDS self-dual codes over Galois rings. We consider a building-up construction of self-dual codes over Galois rings as a GF(q)-analogue of (Kim and Lee, J Combin Theory ser A, 105:79-95). We give a necessary and sufficient condition on which the building-up construction holds. We construct MDS self-dual codes of lengths up to 8 over GR(32,2), GR(33,2) and GR(34,2), and near-MDS self-dual codes of length 10 over these rings. In a similar manner, over GR(52,2), GR(53,2) and GR(72,2), we construct MDS self-dual codes of lengths up to 10 and near-MDS self-dual codes of length 12. Furthermore, over GR(112,2) we have MDS self-dual codes of lengths up to 12. © 2007 Springer Science+Business Media, LLC.
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