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Paper Abstract and Keywords
Presentation 2007-07-20 11:25
Constructing Self-Dual Normal Bases in Odd-Degree Extension Field
Yumi Sakemi, Hiroaki Nasu, Ryo Nanba, Yasuyuki Nogami, Yoshitaka Morikawa (Okayama Univ.) IT2007-19
Abstract (in Japanese) (See Japanese page) 
(in English) A self-dual normal basis only exists in odd-degree extension field when characteristic $p$ is an odd prime.
However, a method to construct it systematically has not been given.
In this paper, we show a method for constructing a self-dual normal basis in an arbitrary extension field $\F{p}{m}$ such that $4p$ does not divide $m(p-1)$ and $m$ is odd by using a special class of Gauss period normal bases. Then, it is also shown that the vector representations with the self-dual and Gauss period normal bases are easily translated to each other.
Keyword (in Japanese) (See Japanese page) 
(in English) extension field / self dual normal / Gauss period normal basis / / / / /  
Reference Info. IEICE Tech. Rep., vol. 107, no. 143, IT2007-19, pp. 23-27, July 2007.
Paper # IT2007-19 
Date of Issue 2007-07-13 (IT) 
ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380
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)
Download PDF IT2007-19

Conference Information
Committee IT  
Conference Date 2007-07-19 - 2007-07-20 
Place (in Japanese) (See Japanese page) 
Place (in English) Kobe Univ. 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Freshman ssesion, general 
Paper Information
Registration To IT 
Conference Code 2007-07-IT 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Constructing Self-Dual Normal Bases in Odd-Degree Extension Field 
Sub Title (in English)  
Keyword(1) extension field  
Keyword(2) self dual normal  
Keyword(3) Gauss period normal basis  
1st Author's Name Yumi Sakemi  
1st Author's Affiliation Okayama University (Okayama Univ.)
2nd Author's Name Hiroaki Nasu  
2nd Author's Affiliation Okayama University (Okayama Univ.)
3rd Author's Name Ryo Nanba  
3rd Author's Affiliation Okayama University (Okayama Univ.)
4th Author's Name Yasuyuki Nogami  
4th Author's Affiliation Okayama University (Okayama Univ.)
5th Author's Name Yoshitaka Morikawa  
5th Author's Affiliation Okayama University (Okayama Univ.)
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Date Time 2007-07-20 11:25:00 
Presentation Time 25 
Registration for IT 
Paper # IEICE-IT2007-19 
Volume (vol) IEICE-107 
Number (no) no.143 
Page pp.23-27 
#Pages IEICE-5 
Date of Issue IEICE-IT-2007-07-13 

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