We introduce an altered version of the four-circulant construction over group rings for self-dual codes. We consider this construction over the binary field, the rings F2 + uF2 and F4 + uF4 using groups of orders 3, 7, 9, 13, and 15. Through these constructions and their extensions, we find binary self-dual codes of lengths 32, 40, 56, 64, 68 and 80, all of which are extremal or optimal. In particular, we find five new self-dual codes with parameters [56, 28, 10], twenty-three extremal binary self-dual codes of length 68 with new weight enumerators and fifteen new self-dual codes with parameters [80, 40, 14].
|Original language||English (US)|
|Number of pages||19|
|Journal||Australasian Journal of Combinatorics|
|State||Published - Jun 2022|
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics