Recently there has been tremendous interest in self-dual codes over finite rings, specifically the rings ℤ 2k. In this paper, we investigate double circulant self-dual codes over ℤ 2k for small k and short lengths. In particular, we give a classification of the extremal double circulant codes. Using invariant theory, a basis for the space of invariants to which the Hamming weight enumerators belong is given for self-dual codes over ℤ 6, ℤ 8, ℤ 10, and ℤ 12.
- Extremal self-dual codes
- Ring codes
- Weight enumerators
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences