Hadamard matrices of order 32 and extremal ternary self-dual codes
K Betsumiya, M Harada, H Kimura - Designs, Codes and Cryptography, 2011 - Springer
K Betsumiya, M Harada, H Kimura
Designs, Codes and Cryptography, 2011•SpringerA 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.
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.
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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