Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 407-422 |
| Number of pages | 16 |
| Journal | Journal of Combinatorial Theory. Series A |
| Volume | 115 |
| Issue number | 3 |
| DOIs | |
| State | Published - Apr 2008 |
Bibliographical note
Funding Information:* Fax: +1 604 291 4947. E-mail addresses: [email protected] (H. Lee), [email protected] (Y. Lee). 1 The author was supported by the Ewha Womans University Research Grant. 2 The author was supported by NSERC.
Keywords
- Finite ring
- MDR codes
- MDS codes
- Near MDR codes
- Near MDS
- Self-dual codes
- Self-orthogonal codes