By the Assmus and Mattson theorem, the codewords of each nontrivial weight in an extremal doubly even self-dual code of length 24m form a self-orthogonal 5-design. In this paper, we study the codes constructed from self-orthogonal 5-designs with the same parameters as the above 5-designs. We give some parameters of a self-orthogonal 5-design whose existence is equivalent to that of an extremal doubly even self-dual code of length 24m for (Formula presented) and (Formula presented.), then it is shown that an extremal doubly even self-dual code of length 24m is generated by codewords of weight 4k.
- Extremal doubly even Self-dual code
- Self-orthogonal (Formula presented.)-design
- Weight enumerator
ASJC Scopus subject areas
- Computer Science Applications
- Applied Mathematics