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

3 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

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10.1002/jcd.10057

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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.

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KW - Hadamard design

KW - Hadamard matrix

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Some hadamard matrices of order 32 and their binary codes

Abstract

Keywords

ASJC Scopus subject areas

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