Abstract
Most of the research on formally self-dual (f.s.d.) codes has been developed for binary f.s.d. even codes, but only limited research has been done for binary f.s.d. odd codes. In this article we complete the classification of binary f.s.d. odd codes of lengths up to 14. We also classify optimal binary f.s.d. odd codes of length 18 and 24, so our result completes the classification of binary optimal f.s.d. odd codes of lengths up to 26. For this classification we first find a relation between binary f.s.d. odd codes and binary f.s.d. even codes, and then we use this relation and the known classification results on binary f.s.d. even codes. We also classify (possibly) optimal binary double circulant f.s.d. odd codes of lengths up to 40.
| Original language | English |
|---|---|
| Pages (from-to) | 141-150 |
| Number of pages | 10 |
| Journal | Designs, Codes, and Cryptography |
| Volume | 61 |
| Issue number | 2 |
| DOIs | |
| State | Published - Nov 2011 |
Bibliographical note
Funding Information:Acknowledgments The authors thank the referees for their valuable comments which improved the clarity of this article. Sunghyu Han was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2010-0007232). Heisook Lee was supported by the Brain Korea 21 Ewha Mathematical Research Team 06A2706. Yoonjin Lee was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 20090059867).
Keywords
- Formally self-dual codes
- Formally self-dual even codes
- Formally self-dual odd codes