Construction of MDS self-dual codes over Galois rings

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 [20]. 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. Key words. Self-dual code, Galois ring, MDS code.

• Type: Conference
• Year: 2007
• Where: DCC
• Authors: Jon-Lark Kim, Yoonjin Lee
• Keywords: Computer Graphics, DCC 2007, MDS Self-dual Codes, Near-MDS Self-dual Codes, Nontrivial Mds