It is known that all doubly-even self-dual codes of lengths 8 or 16, and the extended Golay code, can be constructed from some binary Hadamard matrix of orders 8, 16, and 24, respectively. In this note, we demonstrate that every extremal doubly-even self-dual [32,16,8] code can be constructed from some binary Hadamard matrix of order 32.
- Exteremal doubly-even self-dual code
- Hadamard design
- Hadamard matrix
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics