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Paper Abstract and Keywords
Presentation 2018-05-18 10:50
Hadamard-type Matrices on Finite Fields and Complete Complementary Codes
Tetsuya Kojima (NIT, Tokyo College) IT2018-7 EMM2018-7
Abstract (in Japanese) (See Japanese page) 
(in English) Hadamard matrix is defined as a square matrix where any components are $-1$ or $+1$, and where any pairs of rows are mutually orthogonal. In this study, we consider the similar matrix on finite field $GF(p)$ where $p$ is an odd prime. In such a matrix, every component is one of the integers on $GF(p) backslash {0}$, that is, ${ 1, 2, ldots, p-1}$. Any additions and multiplications should be executed under modulo $p$. In this paper, a method to generate such matrices is proposed. In addition, the paper includes the applications to generate $n$-shift orthogonal sequences and complete complementary codes. The generated complete complementary code is a family of sets of multi-valued sequences on $GF(p)$, where the number of sequence sets, the number of sequences in each sequence set and the sequence length depend on various divisors of $p-1$. To the best of the author's knowledge, such complete complementary codes with various parameters have not been proposed in previous studies.
Keyword (in Japanese) (See Japanese page) 
(in English) Hadamard-type matrix / finite field / odd prime number / n-shift orthogonal sequence / complete complementary code / cyclic group / /  
Reference Info. IEICE Tech. Rep., vol. 118, no. 31, IT2018-7, pp. 35-40, May 2018.
Paper # IT2018-7 
Date of Issue 2018-05-10 (IT, EMM) 
ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380
Download PDF IT2018-7 EMM2018-7

Conference Information
Committee IT EMM  
Conference Date 2018-05-17 - 2018-05-18 
Place (in Japanese) (See Japanese page) 
Place (in English) Ookayama Campus, Tokyo Institute of Technology 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Information Security, Information Theory, Information Hiding, etc. 
Paper Information
Registration To IT 
Conference Code 2018-05-IT-EMM 
Language English (Japanese title is available) 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Hadamard-type Matrices on Finite Fields and Complete Complementary Codes 
Sub Title (in English)  
Keyword(1) Hadamard-type matrix  
Keyword(2) finite field  
Keyword(3) odd prime number  
Keyword(4) n-shift orthogonal sequence  
Keyword(5) complete complementary code  
Keyword(6) cyclic group  
1st Author's Name Tetsuya Kojima  
1st Author's Affiliation National Institute of Technology, Tokyo College (NIT, Tokyo College)
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Date Time 2018-05-18 10:50:00 
Presentation Time 25 
Registration for IT 
Paper # IEICE-IT2018-7,IEICE-EMM2018-7 
Volume (vol) IEICE-118 
Number (no) no.31(IT), no.32(EMM) 
Page pp.35-40 
#Pages IEICE-6 
Date of Issue IEICE-IT-2018-05-10,IEICE-EMM-2018-05-10 

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