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 |
Copyright and reproduction |
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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IT2014-58 |
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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Topics (in Japanese) |
(See Japanese page) |
Topics (in English) |
general |
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) |
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finite field |
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binary periodic sequence |
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two-level autocorrelation |
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circulant Hadamard matrix |
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Chinese remainder theorem |
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1st Author's Name |
Yoshimasa Oh-hashi |
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Speaker |
Author-1 |
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 |
6 |
Date of Issue |
2015-01-23 (IT) |
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