## A search for Hadamard matrices constructed from Williamson matrices

Venue: | Bull. Institute of Combinatorics and its Applications |

Citations: | 5 - 3 self |

### BibTeX

@ARTICLE{Horton_asearch,

author = {Jeffrey Horton and Christos Koukouvinos and Jennifer Seberry},

title = {A search for Hadamard matrices constructed from Williamson matrices},

journal = {Bull. Institute of Combinatorics and its Applications},

year = {},

pages = {75--88}

}

### OpenURL

### Abstract

Abstract. We describe the implementation of a distributed computer search that uses Williamson’s construction for Hadamard matrices. The search program is used to perform a complete search for matrices of orders 100 through 148. No new results are found, confirming existing results. We are convinced that no further matrices of any order less than 156 may be constructed. For reference purposes, we present tables of Hadamard matrices of orders 100 through 180 constructed using four circulant symmetric (1,−1) matrices in the Williamson array. 1

### Citations

1116 |
Using MPI: Portable Parallel Programming with the Message Passing Interface, 2nd ed
- Gropp, Skjellum
- 1999
(Show Context)
Citation Context ...lient program itself, all communication was performed using low-level networking APIs, sockets [13] on UNIX and Open Transport [3] on the Macintosh, rather than using a package such as PVM [7] or MPI =-=[8]-=- that in some cases can facilitate the construction of distributed programs. Searches for Hadamard matrices of all orders up to and including order 148 have been performed using Williamson’s method im... |

88 |
Vaidy Sunderam. PVM: Parallel Virtual Machine – A User’s Guide and Tutorial for Networked Parallel Computing
- Geist, Beguelin, et al.
- 1994
(Show Context)
Citation Context ...at of the client program itself, all communication was performed using low-level networking APIs, sockets [13] on UNIX and Open Transport [3] on the Macintosh, rather than using a package such as PVM =-=[7]-=- or MPI [8] that in some cases can facilitate the construction of distributed programs. Searches for Hadamard matrices of all orders up to and including order 148 have been performed using Williamson’... |

87 | Hadamard matrices, sequences and block designs
- Seberry, Yamada
- 1992
(Show Context)
Citation Context ...the Williamson array. 1 Introduction An Hadamard matrix H of order n has elements ±1 and satisfies HH T = nIn. These matrices are used extensively in coding and communications [see Seberry and Yamada =-=[12]-=-]. The order of an Hadamard matrix is n ≡ 0 mod 4. The first unsolved case is order 428. We use Williamson’s construction as the basis of our algorithm to construct a distributed computer search for n... |

38 |
UNIX Network Programming – Networking APIs: Sockets and XTI", Volume 1, Second Edition
- Stevens
- 1998
(Show Context)
Citation Context ...e best use of the available resources, and to eliminate any need to install software beyond that of the client program itself, all communication was performed using low-level networking APIs, sockets =-=[13]-=- on UNIX and Open Transport [3] on the Macintosh, rather than using a package such as PVM [7] or MPI [8] that in some cases can facilitate the construction of distributed programs. Searches for Hadama... |

6 |
Hadamard matrices of orders 116 and 232
- Baumert
- 1966
(Show Context)
Citation Context ...vic [4]. – Dokovic [5] reports results of a complete search for orders 4t, t = 29, 31. Only a single non-equivalent solution was found for t = 29 and is equivalent to an earlier result due to Baumert =-=[1]-=-. – Koukouvinos and Kounias [10] report results of a complete search for order 4t, t = 33. These results were later demonstrated to be incomplete by Dokovic [6]. – Koukouvinos and Kounias [9] report t... |

5 |
matrices of order 4n for n
- Williamson
- 1993
(Show Context)
Citation Context ...ent to an earlier result due to Baumert [1]. – Koukouvinos and Kounias [10] report results of a complete search for order 4t, t = 33. These results were later demonstrated to be incomplete by Dokovic =-=[6]-=-. – Koukouvinos and Kounias [9] report that no circulant symmetric Williamson matrices of order 39 exist, a result later demonstrated to be incorrect by Dokovic [6]. – Dokovic [6] reports results of a... |

4 |
There are no circulant symmetric Williamson matrices of order 39
- Koukouvinos, Kounias
- 1990
(Show Context)
Citation Context ... Baumert [1]. – Koukouvinos and Kounias [10] report results of a complete search for order 4t, t = 33. These results were later demonstrated to be incomplete by Dokovic [6]. – Koukouvinos and Kounias =-=[9]-=- report that no circulant symmetric Williamson matrices of order 39 exist, a result later demonstrated to be incorrect by Dokovic [6]. – Dokovic [6] reports results of a complete search for orders 4t,... |

4 |
Hadamard matrices of order 100 and 108
- Sawade
- 1977
(Show Context)
Citation Context ... and will also be discussed briefly. – Baumert and Hall [2] report results of a complete search for orders 4t, t odd and 3 ≤ t ≤ 23. Some incomplete results for higher orders are also given. – Sawade =-=[11]-=- reports results of a complete search for orders 4t, t = 25, 27. The results for t = 25 were later demonstrated to be incomplete by Dokovic [4]. – Dokovic [5] reports results of a complete search for ... |

4 |
Hadamard matrices of the Williamson type of order 4m, m=pq: An exhaustive search for m=33
- Koukouvinos, Kounias
- 1988
(Show Context)
Citation Context ...results of a complete search for orders 4t, t = 29, 31. Only a single non-equivalent solution was found for t = 29 and is equivalent to an earlier result due to Baumert [1]. – Koukouvinos and Kounias =-=[10]-=- report results of a complete search for order 4t, t = 33. These results were later demonstrated to be incomplete by Dokovic [6]. – Koukouvinos and Kounias [9] report that no circulant symmetric Willi... |

3 |
Inside Macintosh: Networking with Open Transport
- Computer
- 1997
(Show Context)
Citation Context ...urces, and to eliminate any need to install software beyond that of the client program itself, all communication was performed using low-level networking APIs, sockets [13] on UNIX and Open Transport =-=[3]-=- on the Macintosh, rather than using a package such as PVM [7] or MPI [8] that in some cases can facilitate the construction of distributed programs. Searches for Hadamard matrices of all orders up to... |

3 |
matrices of orders 4.29 and 4.31
- Dokovic, Williamson
- 1992
(Show Context)
Citation Context ...r higher orders are also given. – Sawade [11] reports results of a complete search for orders 4t, t = 25, 27. The results for t = 25 were later demonstrated to be incomplete by Dokovic [4]. – Dokovic =-=[5]-=- reports results of a complete search for orders 4t, t = 29, 31. Only a single non-equivalent solution was found for t = 29 and is equivalent to an earlier result due to Baumert [1]. – Koukouvinos and... |

1 | Koukouvinosand Stratis Kounias. Hadamard matrices of the Williamson type of order 4.m, m = pq: An exhaustive search for m = 33 - Christos - 1988 |

1 |
Note on Williamson matrices of orders 25 and 37
- Dokovic
- 1995
(Show Context)
Citation Context ...lete results for higher orders are also given. – Sawade [11] reports results of a complete search for orders 4t, t = 25, 27. The results for t = 25 were later demonstrated to be incomplete by Dokovic =-=[4]-=-. – Dokovic [5] reports results of a complete search for orders 4t, t = 29, 31. Only a single non-equivalent solution was found for t = 29 and is equivalent to an earlier result due to Baumert [1]. – ... |