Some hadamard matrices of order 32 and their binary codes

Makoto Araya; Masaaki Harada; Hadi Kharaghani

doi:10.1002/jcd.10057

Some hadamard matrices of order 32 and their binary codes

Makoto Araya, Masaaki Harada, Hadi Kharaghani

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

2 Citations (Scopus)

Abstract

It is known that all doubly-even self-dual codes of lengths 8 or 16, and the extended Golay code, can be constructed from some binary Hadamard matrix of orders 8, 16, and 24, respectively. In this note, we demonstrate that every extremal doubly-even self-dual [32,16,8] code can be constructed from some binary Hadamard matrix of order 32.

Original language	English
Pages (from-to)	142-146
Number of pages	5
Journal	Journal of Combinatorial Designs
Volume	12
Issue number	2
DOIs	https://doi.org/10.1002/jcd.10057
Publication status	Published - 2004 Dec 1
Externally published	Yes

Keywords

2-rank
Exteremal doubly-even self-dual code
Hadamard design
Hadamard matrix

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Access to Document

10.1002/jcd.10057

Fingerprint Dive into the research topics of 'Some hadamard matrices of order 32 and their binary codes'. Together they form a unique fingerprint.

Cite this

@article{bb530f3549354c3bb071142e1b29ec39,

title = "Some hadamard matrices of order 32 and their binary codes",

abstract = "It is known that all doubly-even self-dual codes of lengths 8 or 16, and the extended Golay code, can be constructed from some binary Hadamard matrix of orders 8, 16, and 24, respectively. In this note, we demonstrate that every extremal doubly-even self-dual [32,16,8] code can be constructed from some binary Hadamard matrix of order 32.",

keywords = "2-rank, Exteremal doubly-even self-dual code, Hadamard design, Hadamard matrix",

author = "Makoto Araya and Masaaki Harada and Hadi Kharaghani",

year = "2004",

month = dec,

day = "1",

doi = "10.1002/jcd.10057",

language = "English",

volume = "12",

pages = "142--146",

journal = "Journal of Combinatorial Designs",

issn = "1063-8539",

publisher = "John Wiley and Sons Inc.",

number = "2",

}

TY - JOUR

T1 - Some hadamard matrices of order 32 and their binary codes

AU - Araya, Makoto

AU - Harada, Masaaki

AU - Kharaghani, Hadi

PY - 2004/12/1

Y1 - 2004/12/1

N2 - It is known that all doubly-even self-dual codes of lengths 8 or 16, and the extended Golay code, can be constructed from some binary Hadamard matrix of orders 8, 16, and 24, respectively. In this note, we demonstrate that every extremal doubly-even self-dual [32,16,8] code can be constructed from some binary Hadamard matrix of order 32.

AB - It is known that all doubly-even self-dual codes of lengths 8 or 16, and the extended Golay code, can be constructed from some binary Hadamard matrix of orders 8, 16, and 24, respectively. In this note, we demonstrate that every extremal doubly-even self-dual [32,16,8] code can be constructed from some binary Hadamard matrix of order 32.

KW - 2-rank

KW - Exteremal doubly-even self-dual code

KW - Hadamard design

KW - Hadamard matrix

UR - http://www.scopus.com/inward/record.url?scp=1542334763&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1542334763&partnerID=8YFLogxK

U2 - 10.1002/jcd.10057

DO - 10.1002/jcd.10057

M3 - Article

AN - SCOPUS:1542334763

VL - 12

SP - 142

EP - 146

JO - Journal of Combinatorial Designs

JF - Journal of Combinatorial Designs

SN - 1063-8539

IS - 2

ER -