𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the classification of Hadamard matrices of order 32

✍ Scribed by H. Kharaghani; B. Tayfeh-Rezaie

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
100 KB
Volume
18
Category
Article
ISSN
1063-8539

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

All equivalence classes of Hadamard matrices of order at most 28 have been found by 1994. Order 32 is where a combinatorial explosion occurs on the number of Hadamard matrices. We find all equivalence classes of Hadamard matrices of order 32 which are of certain types. It turns out that there are exactly 13, 680, 757 Hadamard matrices of one type and 26, 369 such matrices of another type. Based on experience with the classification of Hadamard matrices of smaller order, it is expected that the number of the remaining two types of these matrices, relative to the total number of Hadamard matrices of order 32, to be insignificant. © 2009 Wiley Periodicals, Inc. J Combin Designs 18:328–336, 2010

📜 SIMILAR VOLUMES

Some Hadamard matrices of order 32 and t
Some Hadamard matrices of order 32 and their binary codes
✍ Makoto Araya; Masaaki Harada; Hadi Kharaghani 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 70 KB

## 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 const

Hadamard matrices of small order and Yan
Hadamard matrices of small order and Yang conjecture
✍ Dragomir Ž. Ðoković 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 79 KB

## Abstract We show that 138 odd values of __n__<10000 for which a Hadamard matrix of order 4__n__ exists have been overlooked in the recent handbook of combinatorial designs. There are four additional odd __n__=191, 5767, 7081, 8249 in that range for which Hadamard matrices of order 4__n__ exist.

On the self-dual 5-codes constructed fro
On the self-dual 5-codes constructed from Hadamard matrices of order 24
✍ Masaaki Harada 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 71 KB

## Abstract There are exactly 60 inequivalent Hadamard matrices of order 24. In this note, we give a classification of the self‐dual 𝔽~5~‐codes of length 48 constructed from the Hadamard matrices of order 24. © 2004 Wiley Periodicals, Inc.

On the asymptotic existence of complex H
On the asymptotic existence of complex Hadamard matrices
✍ R. Craigen; W. H. Holzmann; H. Kharaghani 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 159 KB 👁 2 views

Let N = N (q) be the number of nonzero digits in the binary expansion of the odd integer q. A construction method is presented which produces, among other results, a block circulant complex Hadamard matrix of order 2 α q, where α ≥ 2N -1. This improves a recent result of Craigen regarding the asympt

On Hadamard matrices of order 2(p+1) wit
On Hadamard matrices of order 2(p+1) with an automorphism of odd prime order p
✍ Daniel B. Dalan; Masaaki Harada; Akihiro Munemasa 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 126 KB

## Abstract In this paper, we investigate Hadamard matrices of order 2(p + 1) with an automorphism of odd prime order __p__. In particular, the classification of such Hadamard matrices for the cases __p__ = 19 and 23 is given. Self‐dual codes related to such Hadamard matrices are also investigated.

Skew-Hadamard matrices of orders 436, 58
Skew-Hadamard matrices of orders 436, 580, and 988 exist
✍ Dragomir Ž. Đoković 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 98 KB

## Abstract We construct two difference families on each of the cyclic groups of order 109, 145, and 247, and use them to construct skew‐Hadamard matrices of orders 436, 580, and 988. Such difference families and matrices are constructed here for the first time. The matrices are constructed by usin