TY - JOUR
T1 - Construction of MDS self-dual codes over Galois rings
AU - Kim, Jon Lark
AU - Lee, Yoonjin
N1 - Funding Information:
Acknowledgments The authors thank the anonymous referees for comments and suggestions which helped to improve the paper. J.-L. Kim was supported in part by a Project Completion Grant from the University of Louisville and Y. Lee was supported by NSERC.
PY - 2007/11
Y1 - 2007/11
N2 - 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.
AB - 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.
KW - Galois ring
KW - MDS code
KW - Self-dual code
UR - http://www.scopus.com/inward/record.url?scp=34748881326&partnerID=8YFLogxK
U2 - 10.1007/s10623-007-9117-y
DO - 10.1007/s10623-007-9117-y
M3 - Article
AN - SCOPUS:34748881326
SN - 0925-1022
VL - 45
SP - 247
EP - 258
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 2
ER -