Construction of MDS self-dual codes over Galois rings

被引：0
作者：
Jon-Lark Kim
Yoonjin Lee
机构：
[1] University of Louisville,Department of Mathematics
[2] Ewha W. University,Department of Mathematics
来源：
Designs, Codes and Cryptography | 2007年 / 45卷
关键词：
Self-dual code; Galois ring; MDS code; 94B05; 13H99;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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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页码：247 / 258
页数：11
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