TY - JOUR
T1 - Construction of self-dual codes over finite rings Zpm
AU - Lee, Heisook
AU - Lee, Yoonjin
N1 - Funding Information:
* Fax: +1 604 291 4947. E-mail addresses: hsllee@ewha.ac.kr (H. Lee), yoonjinl@ewha.ac.kr (Y. Lee). 1 The author was supported by the Ewha Womans University Research Grant. 2 The author was supported by NSERC.
PY - 2008/4
Y1 - 2008/4
N2 - We present an efficient method for constructing self-dual or self-orthogonal codes over finite rings Zpm (or Zm) with p an odd prime and m a positive integer. This is an extension of the previous work [J.-L. Kim, Y. Lee, Euclidean and Hermitian self-dual MDS codes over large finite fields, J. Combin. Theory Ser. A 105 (2004) 79-95] over large finite fields GF (pm) to finite rings Zpm (or Zm). Using this method we construct self-dual or self-orthogonal codes of length at least up to 10 over various finite rings Zpm or Zp q with q an odd prime, where pm = 25, 125, 169, 289 and p q = 65, 85. All the self-dual codes we obtained are MDS, MDR, near MDS, or near MDR codes.
AB - We present an efficient method for constructing self-dual or self-orthogonal codes over finite rings Zpm (or Zm) with p an odd prime and m a positive integer. This is an extension of the previous work [J.-L. Kim, Y. Lee, Euclidean and Hermitian self-dual MDS codes over large finite fields, J. Combin. Theory Ser. A 105 (2004) 79-95] over large finite fields GF (pm) to finite rings Zpm (or Zm). Using this method we construct self-dual or self-orthogonal codes of length at least up to 10 over various finite rings Zpm or Zp q with q an odd prime, where pm = 25, 125, 169, 289 and p q = 65, 85. All the self-dual codes we obtained are MDS, MDR, near MDS, or near MDR codes.
KW - Finite ring
KW - MDR codes
KW - MDS codes
KW - Near MDR codes
KW - Near MDS
KW - Self-dual codes
KW - Self-orthogonal codes
UR - http://www.scopus.com/inward/record.url?scp=39749123893&partnerID=8YFLogxK
U2 - 10.1016/j.jcta.2007.07.001
DO - 10.1016/j.jcta.2007.07.001
M3 - Article
AN - SCOPUS:39749123893
SN - 0097-3165
VL - 115
SP - 407
EP - 422
JO - Journal of Combinatorial Theory. Series A
JF - Journal of Combinatorial Theory. Series A
IS - 3
ER -