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Constructing New Turyn Type Sequence...

London, Stephen.

Constructing New Turyn Type Sequences, T-Sequences and Hadamard Matrices.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Constructing New Turyn Type Sequences, T-Sequences and Hadamard Matrices.
作者:	London, Stephen.
面頁冊數:	64 p.
附註:	Source: Dissertation Abstracts International, Volume: 74-12(E), Section: B.
附註:	Adviser: Vera Pless.
Contained By:	Dissertation Abstracts International74-12B(E).
標題:	Mathematics.
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3573367
ISBN:	9781303435423

Constructing New Turyn Type Sequences, T-Sequences and Hadamard Matrices.
London, Stephen.

Constructing New Turyn Type Sequences, T-Sequences and Hadamard Matrices. - 64 p.

Source: Dissertation Abstracts International, Volume: 74-12(E), Section: B.

Thesis (Ph.D.)--University of Illinois at Chicago, 2013.

This study investigates computational methods for the construction and enumeration of Turyn Type sequences, which can be used to construct T-Sequences and Hadamard matrices. Extending and optimizing an approach originally introduced by Hadi Kharaghani, we have performed the most comprehensive search for Turyn Type sequences to date. We have checked the enumeration of Turyn Type sequences recently reported by Best et al. [3] and found it to be correct for lengths up to 30, but identified 66 additional sequences that were missed for length 32. We then randomly selected and evaluated approximately 132 of the search space to estimate the total number of Turyn Type sequences of lengths 34 and 36. In order to identify longer sequences, the search algorithm was further optimized by restricting the values of some parameters. This approach allowed the identification of 119 new Turyn Type sequences of lengths 34 and 101 new Turyn Type Sequences of length 36. We verified that each sequence leads to a unique Hadamard matrix. This calculation has allowed the identification of 101 new Hadamard matrices of order 428; only one had been identified prior to this analysis. We have also found 10 Turyn Type sequences of length 38. This directly leads to 10 of the 11 known T-sequences of length 113, with the other being discovered by Best et al. [3]. Finally, we discovered the first three Turyn Type sequences of length 40 which are the longest known Turyn Type sequences.

ISBN: 9781303435423Subjects--Topical Terms:

184409
Mathematics.

Constructing New Turyn Type Sequences, T-Sequences and Hadamard Matrices.
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245 1 0 $a Constructing New Turyn Type Sequences, T-Sequences and Hadamard Matrices.
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500 $a Source: Dissertation Abstracts International, Volume: 74-12(E), Section: B.
500 $a Adviser: Vera Pless.
502 $a Thesis (Ph.D.)--University of Illinois at Chicago, 2013.
520 $a This study investigates computational methods for the construction and enumeration of Turyn Type sequences, which can be used to construct T-Sequences and Hadamard matrices. Extending and optimizing an approach originally introduced by Hadi Kharaghani, we have performed the most comprehensive search for Turyn Type sequences to date. We have checked the enumeration of Turyn Type sequences recently reported by Best et al. [3] and found it to be correct for lengths up to 30, but identified 66 additional sequences that were missed for length 32. We then randomly selected and evaluated approximately 132 of the search space to estimate the total number of Turyn Type sequences of lengths 34 and 36. In order to identify longer sequences, the search algorithm was further optimized by restricting the values of some parameters. This approach allowed the identification of 119 new Turyn Type sequences of lengths 34 and 101 new Turyn Type Sequences of length 36. We verified that each sequence leads to a unique Hadamard matrix. This calculation has allowed the identification of 101 new Hadamard matrices of order 428; only one had been identified prior to this analysis. We have also found 10 Turyn Type sequences of length 38. This directly leads to 10 of the 11 known T-sequences of length 113, with the other being discovered by Best et al. [3]. Finally, we discovered the first three Turyn Type sequences of length 40 which are the longest known Turyn Type sequences.
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