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

Koichi Betsumiya, Masaaki Harada, Hiroshi Kimura

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)203-214
Number of pages12
JournalDesigns, Codes, and Cryptography
Issue number2
Publication statusPublished - 2011 Feb


  • Extremal self-dual code
  • Hadamard matrix
  • Paley-Hadamard matrix
  • Ternary code


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