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Construction of MDS self-dual codes over Galois rings

Title
Construction of MDS self-dual codes over Galois rings
Authors
Kim J.-L.Lee Y.
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2007
Journal Title
Designs, Codes, and Cryptography
ISSN
0925-1022JCR Link
Citation
vol. 45, no. 2, pp. 247 - 258
Indexed
SCI; SCIE; SCOPUS WOS scopus
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. © 2007 Springer Science+Business Media, LLC.
DOI
10.1007/s10623-007-9117-y
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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