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

Koichi Betsumiya; Masaaki Harada; Hiroshi Kimura

doi:10.1007/s10623-010-9403-y

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

Koichi Betsumiya, Masaaki Harada, Hiroshi Kimura

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	203-214
Number of pages	12
Journal	Designs, Codes, and Cryptography
Volume	58
Issue number	2
DOIs	https://doi.org/10.1007/s10623-010-9403-y
Publication status	Published - 2011 Feb 1
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Computer Science Applications
Applied Mathematics

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10.1007/s10623-010-9403-y

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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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AU - Kimura, Hiroshi

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Y1 - 2011/2/1

N2 - 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.

AB - 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.

KW - Extremal self-dual code

KW - Hadamard matrix

KW - Paley-Hadamard matrix

KW - Ternary code

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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