In this paper it is shown that the weight enumerator of a bordered double circulant self-dual code can be obtained from those of a pure double circulant self-dual code and its shadow through a relationship between bordered and pure double circulant codes. As applications, a restriction on the weight enumerators of some extremal double circulant codes is determined and a uniqueness proof of extremal double circulant self-dual codes of length 46 is given. New extremal singly-even [44, 22, 8] double circulant codes are constructed. These codes have weight enumerators for which extremal codes were not previously known to exist.
ASJC Scopus subject areas
- Computer Science Applications
- Applied Mathematics