𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Hadamard matrices of small order and Yang conjecture

✍ Scribed by Dragomir Ž. Ðoković

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

No coin nor oath required. For personal study only.

✦ Synopsis

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. There is a unique equivalence class of near‐normal sequences NN(36), and the same is true for NN(38) and NN(40). This means that the Yang conjecture on the existence of near‐normal sequences NN(n) has been verified for all even n⩽40, but it still remains open. © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 254–259, 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

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

On the classification of Hadamard matric
On the classification of Hadamard matrices of order 32
✍ H. Kharaghani; B. Tayfeh-Rezaie 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 100 KB 👁 1 views

## 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

Enumeration of generalized Hadamard matr
Enumeration of generalized Hadamard matrices of order 16 and related designs
✍ P. B. Gibbons; R. Mathon 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 142 KB

## Abstract We investigate signings of symmetric GDD($16 \times 2^i$, 16, $2^{4-i}$)s over $Z\_2$ for $1 \le i \le 3$. Beginning with $i=1$, at each stage of this process a signing of a GDD($16 \times 2^i$, 16, $2^{4-i}$) produces a GDD($16 \times 2^{i+1}$, 16, $2^{4-i-1}$). The initial GDDs ($i=1$

Weaving hadamard matrices with maximum e
Weaving hadamard matrices with maximum excess and classes with small excess
✍ R. Craigen; H. Kharaghani 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 165 KB

## Abstract Weaving is a matrix construction developed in 1990 for the purpose of obtaining new weighing matrices. Hadamard matrices obtained by weaving have the same orders as those obtained using the Kronecker product, but weaving affords greater control over the internal structure of matrices co