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Paper Abstract and Keywords
Presentation 2015-01-30 14:55
Proof of Conjecture on Nonexistence of Circulant Hadamard Matrices for Order > 4
Yoshimasa Oh-hashi IT2014-58
Abstract (in Japanese) (See Japanese page) 
(in English) There are various kinds of binary periodic sequences with the two-level autocorrelation function. However, in case of the
binary orthogonal periodic sequences, Turyn and Imai et al. have conjectured that there exist only sequences with period 4, i.e., the circulant Hadamard matrices exist for order 4 only. In this report, it is described that the residue rings of polynomials whose elements correspond to the p-ary periodic sequences are isomorphic to not only the direct product rings by means of the Chinese remainder theorem for polynomials, but also the circulant matrix rings. Applying the linear algebra, a part of the proof of the conjecture is presented.
Keyword (in Japanese) (See Japanese page) 
(in English) finite field / binary periodic sequence / two-level autocorrelation / circulant Hadamard matrix / Chinese remainder theorem / / /  
Reference Info. IEICE Tech. Rep., vol. 114, no. 438, IT2014-58, pp. 23-28, Jan. 2015.
Paper # IT2014-58 
Date of Issue 2015-01-23 (IT) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
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All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
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Conference Information
Committee IT  
Conference Date 2015-01-30 - 2015-01-30 
Place (in Japanese) (See Japanese page) 
Place (in English)  
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Paper Information
Registration To IT 
Conference Code 2015-01-IT 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Proof of Conjecture on Nonexistence of Circulant Hadamard Matrices for Order > 4 
Sub Title (in English)  
Keyword(1) finite field  
Keyword(2) binary periodic sequence  
Keyword(3) two-level autocorrelation  
Keyword(4) circulant Hadamard matrix  
Keyword(5) Chinese remainder theorem  
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1st Author's Name Yoshimasa Oh-hashi  
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Date Time 2015-01-30 14:55:00 
Presentation Time 25 minutes 
Registration for IT 
Paper # IT2014-58 
Volume (vol) vol.114 
Number (no) no.438 
Page pp.23-28 
#Pages
Date of Issue 2015-01-23 (IT) 


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