Abstract
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.
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Communicated by J. D. Key.
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Betsumiya, K., Harada, M. & Kimura, H. Hadamard matrices of order 32 and extremal ternary self-dual codes. Des. Codes Cryptogr. 58, 203–214 (2011). https://doi.org/10.1007/s10623-010-9403-y
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DOI: https://doi.org/10.1007/s10623-010-9403-y