Construction of MDS self-dual codes over Galois rings
Construction of MDS self-dual codes over Galois rings
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DOI：
10.1007/s10623-007-9117-y
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发表时间：
2007-11
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影响因子：
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通讯作者：
Jon-Lark Kim;Yoonjin Lee
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文献类型：
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作者：
Jon-Lark Kim;Yoonjin Lee
本文的目的是构造伽罗瓦环上的非平凡MDS自对偶码。我们考虑了伽罗瓦环上自对偶码的一个GF(q)-模拟（Kim and Lee, J .组合理论学报，105:79-95）。给出了建立式成立的充分必要条件。我们在GR（32,2）、GR（32,2）和GR（34,2）上构造了长度为8的MDS自对偶码，并在这些环上构造了长度为10的近MDS自对偶码。同样，在GR（52,2）、GR（53,2）和GR（72,2）上，我们构造了长度为10的MDS自对偶码和长度为12的近MDS自对偶码。此外，在GR（112,2）上，我们有长度达12的MDS自对偶码。
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.