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

Access to Document

10.1007/s10623-010-9403-y

Fingerprint Dive into the research topics of 'Hadamard matrices of order 32 and extremal ternary self-dual codes'. Together they form a unique fingerprint.

Cite this

@article{a5b5fa3014f74c18b088f8519c62058d,

title = "Hadamard matrices of order 32 and extremal ternary self-dual codes",

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.",

keywords = "Extremal self-dual code, Hadamard matrix, Paley-Hadamard matrix, Ternary code",

author = "Koichi Betsumiya and Masaaki Harada and Hiroshi Kimura",

year = "2011",

month = feb,

day = "1",

doi = "10.1007/s10623-010-9403-y",

language = "English",

volume = "58",

pages = "203--214",

journal = "Designs, Codes, and Cryptography",

issn = "0925-1022",

publisher = "Springer Netherlands",

number = "2",

}

TY - JOUR

T1 - Hadamard matrices of order 32 and extremal ternary self-dual codes

AU - Betsumiya, Koichi

AU - Harada, Masaaki

AU - Kimura, Hiroshi

PY - 2011/2/1

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

UR - http://www.scopus.com/inward/record.url?scp=79951674473&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79951674473&partnerID=8YFLogxK

U2 - 10.1007/s10623-010-9403-y

DO - 10.1007/s10623-010-9403-y

M3 - Article

AN - SCOPUS:79951674473

VL - 58

SP - 203

EP - 214

JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

SN - 0925-1022

IS - 2

ER -