Hadamard matrices of order 32 and extremal ternary self-dual codes

A ternary self-dual code can be constructed from a Hadamard matrix of order congruent to 8 modulo 12. In this paper, we show that the Paley-Hadamard matrix is the only Hadamard matrix of order 32 which gives an extremal self-dual code of length 64. This gives a coding theoretic characterization of the Paley-Hadamard matrix of order 32.

• Type: Journal
• Year: 2011
• Where: DCC
• Authors: Koichi Betsumiya, Masaaki Harada, Hiroshi Kimura
• Keywords: Computer Graphics, DCC 2011, Hadamard Matrix, Self-dual Code, Ternary Self-dual Code