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Characterization and synthesis of self-complementary normal bases in finite fields

Abraham Lempel
1988 Linear Algebra and its Applications  
A finite extension Q, = GF( 9") of a finite field F = GF( 9) has a self-complementary normal basis over F iff either n is odd or n = 2 (mod 4) and 9 is even.  ...  This paper presents a complete characterization of square matrices A of order n over F such that the set { A9'):;; is a self-complementary normal basis of a matrix representation of Cp over F.  ...  In this paper we deal with bases of Q, over F which are both self-complementary and normal (for short, SCN bases).  ... 
doi:10.1016/0024-3795(88)90171-1 fatcat:4hwm7yoooff77min2me2ourj4i

Characterization of self-complementary symmetric digraphs

Hong Zhang
1996 Discrete Mathematics  
The class of self-complementary symmetric digraphs is characterized and it is shown that the number of vertices of such a digraph is an odd prime power. Let G be a group and H be a subset of G.  ...  Construction A family of self-complementary symmetric digraphs can be constructed based on finite fields. The construction is similar to those in [2, 4] .  ...  Let p be a prime and F the finite field with p" elements.  ... 
doi:10.1016/0012-365x(95)00236-p fatcat:kqvskz5q7rdk3mb3vnc6td3l6a

Page 1444 of Mathematical Reviews Vol. , Issue 98C [page]

1998 Mathematical Reviews  
Moreover, they show that if 8 and y generate dual normal bases then the CCP of # and y generates a self-complementary normal basis.  ...  thus how to obtain a self-complementary normal basis.  ... 

Page 5968 of Mathematical Reviews Vol. , Issue 89K [page]

1989 Mathematical Reviews  
McConnel (1-TN) 89k:11126 11T30 Lempel, Abraham (IL-TECH-C) Characterization and synthesis of self-complementary normal bases in finite fields. Linear Algebra Appl. 98 (1988), 331-346.  ...  A basis Q is self-complementary if Q* = Q. An SCN basis is a normal self-complementary basis. The field ® may be represented by n x n matrices over F.  ... 

Page 4606 of Mathematical Reviews Vol. , Issue 96h [page]

1996 Mathematical Reviews  
The aim of the paper is to construct self-complementary normal ’ 11 NUMBER THEORY 4606 bases, also called self-dual normal bases, in finite fields with characteristic 2.  ...  In the second part the author constructs a self-complementary normal basis over GF(q), where g = 2’, with the help of a normal basis B in GF(q").  ... 

Page 12 of Mathematical Reviews Vol. , Issue 92c [page]

1992 Mathematical Reviews  
Wolfe (Rio Grande, OH) 92c:11148 11T30 12E20 Lempel, Abraham (IL-TECH); Seroussi, Gadiel (1-HPL) Explicit formulas for self-complementary normal bases in certain finite fields. IEEE Trans. Inform.  ...  The authors give explicit formulas for self-complementary normal bases (of p elements) for GF(q’), where p = char(GF(q)). They  ... 

Page 14 of Mathematical Reviews Vol. , Issue 89I [page]

1989 Mathematical Reviews  
(IL-TECH-C) Self-complementary normal bases in finite fields. SIAM J. Discrete Math. 1 (1988), no. 2, 193-198.  ...  A basis is called an SCN basis if it is both self-complementary and normal. The authors prove: The field ® has an SCN basis over F if and only if either (a) n is odd, or (b) n=2 mod 4 and q is even.  ... 

Energy loss of terahertz electromagnetic waves by nano-sized connections in near-self-complementary metallic checkerboard patterns

Keisuke Takano, Yoku Tanaka, Gabriel Moreno, Abdallah Chahadih, Abbas Ghaddar, Xiang-Lei Han, François Vaurette, Yosuke Nakata, Fumiaki Miyamaru, Makoto Nakajima, Masanori Hangyo, Tahsin Akalin
2017 Journal of Applied Physics  
We show that finite conductivity and randomness in a near-self-complementary checkerboard pattern plays a crucial role in producing a frequency-independent energy loss in the terahertz frequency region  ...  When the checkerboard pattern approaches the perfect self-complementary pattern, the perfect conductor approximation spontaneously breaks down, owing to the finite conductivity at the nano- scale connection  ...  At the limit of a perfect self-complementary checkerboard pattern in a realistic system, the finite conductivity and randomness in the structure needs to be considered.  ... 
doi:10.1063/1.4997882 fatcat:gk3w3npgojffpeewazgrsl7cym

Page 2501 of Mathematical Reviews Vol. , Issue 94e [page]

1994 Mathematical Reviews  
Normal selfadjoint bases of finite fields. (Russian. Russian summary) Mat. Zametki 53 (1993), no. 1, 121-127, 157; translation in Math. Notes 53 (1993), no. 1-2, 84-88.  ...  A basis B is called an SCN-basis if it is both self-complementary and normal. In the first part of the paper the author proves the following:  ... 

Analysis of electromagnetic scattering from periodic structures by FEM truncated by anisotropic PML boundary condition

Suomin Cui, Daniel S. Weile
2002 Microwave and optical technology letters (Print)  
The Self-Complementary Strip Grating. A self-complementary strip grating is shown in Figure 6 .  ...  Figure 6 6 Reflected power of the fundamental mode for the self-complementary strip grating Figure 7 7 Reflected power of the fundamental mode for the self-complementary strip grating backed by inhomogenous  ... 
doi:10.1002/mop.10530 fatcat:vckgdrkbzjhehplb5c5njicpoy

Frequency-Independent Response of Self-Complementary Checkerboard Screens

Yoshiro Urade, Yosuke Nakata, Toshihiro Nakanishi, Masao Kitano
2015 Physical Review Letters  
This research resolves a long-standing problem on the electromagnetic response of self-complementary metallic screens with checkerboardlike geometry.  ...  Although Babinet's principle implies that they show a frequency-independent response, this unusual characteristic has not been observed yet due to the singularities of the metallic point contacts in the  ...  Miyamaru for his technical advice in the THz-TDS experiments. We are also grateful to R. C. McPhedran for a useful comment at a conference held in Bordeaux and to H.  ... 
doi:10.1103/physrevlett.114.237401 pmid:26196824 fatcat:hxyem76x6bae5gfdrspp4g255m

Broadband and energy-concentrating terahertz coherent perfect absorber based on a self-complementary metasurface

Yoshiro Urade, Yosuke Nakata, Toshihiro Nakanishi, Masao Kitano
2016 Optics Letters  
We demonstrate that a self-complementary checkerboard-like metasurface works as a broadband coherent perfect absorber (CPA) when symmetrically illuminated by two counter-propagating incident waves.  ...  In addition, we experimentally demonstrate the proposed CPA in the terahertz regime by using a time-domain spectroscopy technique.  ...  The sample was prepared using the instruments at the Kyoto University Nano Technology Hub, as part of the "Nanotechnology Platform Project" sponsored by MEXT in Japan. One of the authors (Y.  ... 
doi:10.1364/ol.41.004472 pmid:27749858 fatcat:ihtawmyoybhx7kqu3dtvrf4xdu

THz ultrastrong light-matter coupling [article]

Giacomo Scalari, Curdin Maissen, Sara Cibella, Roberto Leoni, Christian Reichl, Werner Wegscheider, Mattias Beck, Jérôme Faist
2016 arXiv   pre-print
Record-high values of the normalized light-matter coupling ratio Ω/ω= 0.89 are reached and the system appears highly scalable far into the microwave range.  ...  Cavity photon resonators with ultrastrong light-matter interactions are attracting interest both in semiconductor and superconducting systems displaying the capability to manipulate the cavity quantum  ...  and through the SNF Grant No. 129823 and by the EU commission through the ERC Advanced Grant Quantum Metamaterials in the Ultra Strong Coupling Regime (MUSiC).  ... 
arXiv:1611.09151v1 fatcat:zbwo233z2vfhvi732sj7zadqva

Electrically small multiband antenna based on spoof localized surface plasmons

Rong Lin Shao, Bo Li, Liu Yang, Yong Jin Zhou, Junming Zhao, Wenxuan Tang, Shi Hongyu
2019 EPJ Applied Metamaterials  
Here an electrically small multiband antenna based on spoof localized surface plasmons (LSPs) has been proposed using corrugated ring resonator printed on a thin dielectric substrate with complementary  ...  Such electrically small multiband antenna with high gain is necessary for efficient wireless energy harvesting (WEH), which can find more applications in various areas including Internet of Things (IoT  ...  The normal complementary metallic spiral is shown in Figure 4a , where the length of the spiral arms is the same.  ... 
doi:10.1051/epjam/2019009 fatcat:o3ovlbpzwzaanoolthyzwd4roi

Page 532 of Mathematical Reviews Vol. , Issue 80B [page]

1980 Mathematical Reviews  
Math. 39 (1977), no. 3, 223-251; MR 57 #3134] is extended to the case when the field K of complex multiplications has class number one but the base field is any finite abelian extension of K.  ...  trace map in differential algebras of finite-di- mensional algebras over fields (see Section 1 (c) and (d), and*the author [J.  ... 
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