TY - JOUR
T1 - Binary formally self-dual odd codes
AU - Han, Sunghyu
AU - Lee, Heisook
AU - Lee, Yoonjin
N1 - 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).
PY - 2011/11
Y1 - 2011/11
N2 - 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.
AB - 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.
KW - Formally self-dual codes
KW - Formally self-dual even codes
KW - Formally self-dual odd codes
UR - http://www.scopus.com/inward/record.url?scp=80052971668&partnerID=8YFLogxK
U2 - 10.1007/s10623-010-9444-2
DO - 10.1007/s10623-010-9444-2
M3 - Article
AN - SCOPUS:80052971668
SN - 0925-1022
VL - 61
SP - 141
EP - 150
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 2
ER -