We complete the classification the Lee-extremal self-dual codes over the ring F 2uF 2 of lengths 21 and 22 with a nontrivial automorphism of odd prime order except the case for an automorphism of order 3 with seven cycles, and we partially classify the exceptional case. In particular, we show that there are 138 (respectively, 6723) inequivalent Lee-extremal self-dual codes of length 21 (respectively, 22) with an automorphism of odd prime order. We use the decomposition theory for self-dual codes over F 2uF 2 with an automorphism of odd prime order as the same approaches made by Huffman. And we also use an extension method as a new approach, and the current approach is extending the even subcode part while the fixed subcode part is extended in the authors previous work.
Bibliographical noteFunding Information:
✩ The authors were supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) founded by the Ministry of Education, Science and Technology (2010-0028298), and the second named author was also supported by the National Research Foundation of Korea (NRF) grant founded by the Korea government (MEST) (No. 2011-0015684). * Corresponding author. E-mail addresses: email@example.com (H.J. Kim), firstname.lastname@example.org (Y. Lee).
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Algebra and Number Theory
- Applied Mathematics