Construction of MDS self-dual codes over Galois rings |
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| Authors: | Jon-Lark Kim Yoonjin Lee |
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| Affiliation: | (1) Department of Mathematics, University of Louisville, Louisville, KY 40292, USA;(2) Department of Mathematics, Ewha W. University, 120–750, Seoul, South Korea |
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| Abstract: | 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. |
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| Keywords: | Self-dual code Galois ring MDS code |
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