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

1988
*
Linear Algebra and its Applications
*

A

doi:10.1016/0024-3795(88)90171-1
fatcat:4hwm7yoooff77min2me2ourj4i
*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*). ...##
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Characterization of self-complementary symmetric digraphs

1996
*
Discrete Mathematics
*

The class of

doi:10.1016/0012-365x(95)00236-p
fatcat:kqvskz5q7rdk3mb3vnc6td3l6a
*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. ...##
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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

2017
*
Journal of Applied Physics
*

We show that

doi:10.1063/1.4997882
fatcat:gk3w3npgojffpeewazgrsl7cym
*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. ...##
###
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: ...

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

2002
*
Microwave and optical technology letters (Print)
*

The

doi:10.1002/mop.10530
fatcat:vckgdrkbzjhehplb5c5njicpoy
*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 ...##
###
Frequency-Independent Response of Self-Complementary Checkerboard Screens

2015
*
Physical Review Letters
*

This research resolves a long-standing problem on the electromagnetic response of

doi:10.1103/physrevlett.114.237401
pmid:26196824
fatcat:hxyem76x6bae5gfdrspp4g255m
*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. ...##
###
Broadband and energy-concentrating terahertz coherent perfect absorber based on a self-complementary metasurface

2016
*
Optics Letters
*

We demonstrate that a

doi:10.1364/ol.41.004472
pmid:27749858
fatcat:ihtawmyoybhx7kqu3dtvrf4xdu
*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. ...##
###
THz ultrastrong light-matter coupling
[article]

2016
*
arXiv
*
pre-print

Record-high values of the

arXiv:1611.09151v1
fatcat:zbwo233z2vfhvi732sj7zadqva
*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). ...##
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Electrically small multiband antenna based on spoof localized surface plasmons

2019
*
EPJ Applied Metamaterials
*

Here an electrically small multiband antenna

doi:10.1051/epjam/2019009
fatcat:o3ovlbpzwzaanoolthyzwd4roi
*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. ...##
###
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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