Construction of symmetric Hadamard matrices of order 4v for v = 47, 73, 113
We continue our systematic search for symmetric Hadamard matrices based on the so called propus construction. In a previous paper this search covered the orders 4v with odd v ≤ 41. In this paper we cover the cases v = 43, 45, 47, 49, 51. The odd integers v < 120 for which no symmetric Hadamard ma...
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-01-01
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| Series: | Special Matrices |
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| Online Access: | https://doi.org/10.1515/spma-2018-0002 |
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doaj-1acab1266db444d4a101196519df98542021-10-02T19:10:39ZengDe GruyterSpecial Matrices2300-74512018-01-0161112210.1515/spma-2018-0002spma-2018-0002Construction of symmetric Hadamard matrices of order 4v for v = 47, 73, 113Balonin N. A.0Ðokovic D. Ž.1Karbovskiy D. A.2Saint-Petersburg State University of Aerospace Instrumentation, 67, B. Morskaia St., 190000, Saint-Petersburg, Russian FederationUniversity of Waterloo, Department of Pure Mathematics and Institute for Quantum Computing, Waterloo, Ontario, N2L 3G1, CanadaSaint-Petersburg State University of Aerospace Instrumentation, 67, B. Morskaia St., 190000, Saint-Petersburg, Russian FederationWe continue our systematic search for symmetric Hadamard matrices based on the so called propus construction. In a previous paper this search covered the orders 4v with odd v ≤ 41. In this paper we cover the cases v = 43, 45, 47, 49, 51. The odd integers v < 120 for which no symmetric Hadamard matrices of order 4v are known are the following: 47, 59, 65, 67, 73, 81, 89, 93, 101, 103, 107, 109, 113, 119. By using the propus construction, we found several symmetric Hadamard matrices of order 4v for v = 47, 73, 113.https://doi.org/10.1515/spma-2018-0002symmetric hadamard matricespropus arraycyclic difference familiesdiophantine equations |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Balonin N. A. Ðokovic D. Ž. Karbovskiy D. A. |
| spellingShingle |
Balonin N. A. Ðokovic D. Ž. Karbovskiy D. A. Construction of symmetric Hadamard matrices of order 4v for v = 47, 73, 113 Special Matrices symmetric hadamard matrices propus array cyclic difference families diophantine equations |
| author_facet |
Balonin N. A. Ðokovic D. Ž. Karbovskiy D. A. |
| author_sort |
Balonin N. A. |
| title |
Construction of symmetric Hadamard matrices of order 4v for v = 47, 73, 113 |
| title_short |
Construction of symmetric Hadamard matrices of order 4v for v = 47, 73, 113 |
| title_full |
Construction of symmetric Hadamard matrices of order 4v for v = 47, 73, 113 |
| title_fullStr |
Construction of symmetric Hadamard matrices of order 4v for v = 47, 73, 113 |
| title_full_unstemmed |
Construction of symmetric Hadamard matrices of order 4v for v = 47, 73, 113 |
| title_sort |
construction of symmetric hadamard matrices of order 4v for v = 47, 73, 113 |
| publisher |
De Gruyter |
| series |
Special Matrices |
| issn |
2300-7451 |
| publishDate |
2018-01-01 |
| description |
We continue our systematic search for symmetric Hadamard matrices based on the so called propus construction. In a previous paper this search covered the orders 4v with odd v ≤ 41. In this paper we cover the cases v = 43, 45, 47, 49, 51. The odd integers v < 120 for which no symmetric Hadamard matrices of order 4v are known are the following: 47, 59, 65, 67, 73, 81, 89, 93, 101, 103, 107, 109, 113, 119. By using the propus construction, we found several symmetric Hadamard matrices of order 4v for v = 47, 73, 113. |
| topic |
symmetric hadamard matrices propus array cyclic difference families diophantine equations |
| url |
https://doi.org/10.1515/spma-2018-0002 |
| work_keys_str_mv |
AT baloninna constructionofsymmetrichadamardmatricesoforder4vforv4773113 AT ðokovicdz constructionofsymmetrichadamardmatricesoforder4vforv4773113 AT karbovskiyda constructionofsymmetrichadamardmatricesoforder4vforv4773113 |
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1716848023341891584 |