2,103 research outputs found
Weighing matrices and spherical codes
Mutually unbiased weighing matrices (MUWM) are closely related to an
antipodal spherical code with 4 angles. In the present paper, we clarify the
relationship between MUWM and the spherical sets, and give the complete
solution about the maximum size of a set of MUWM of weight 4 for any order.
Moreover we describe some natural generalization of a set of MUWM from the
viewpoint of spherical codes, and determine several maximum sizes of the
generalized sets. They include an affirmative answer of the problem of Best,
Kharaghani, and Ramp.Comment: Title is changed from "Association schemes related to weighing
matrices
Classification of generalized Hadamard matrices H(6,3) and quaternary Hermitian self-dual codes of length 18
All generalized Hadamard matrices of order 18 over a group of order 3,
H(6,3), are enumerated in two different ways: once, as class regular symmetric
(6,3)-nets, or symmetric transversal designs on 54 points and 54 blocks with a
group of order 3 acting semi-regularly on points and blocks, and secondly, as
collections of full weight vectors in quaternary Hermitian self-dual codes of
length 18. The second enumeration is based on the classification of Hermitian
self-dual [18,9] codes over GF(4), completed in this paper. It is shown that up
to monomial equivalence, there are 85 generalized Hadamard matrices H(6,3), and
245 inequivalent Hermitian self-dual codes of length 18 over GF(4).Comment: 17 pages. Minor revisio
A survey of complex generalized weighing matrices and a construction of quantum error-correcting codes
Some combinatorial designs, such as Hadamard matrices, have been extensively
researched and are familiar to readers across the spectrum of Science and
Engineering. They arise in diverse fields such as cryptography, communication
theory, and quantum computing. Objects like this also lend themselves to
compelling mathematics problems, such as the Hadamard conjecture. However,
complex generalized weighing matrices, which generalize Hadamard matrices, have
not received anything like the same level of scrutiny. Motivated by an
application to the construction of quantum error-correcting codes, which we
outline in the latter sections of this paper, we survey the existing literature
on complex generalized weighing matrices. We discuss and extend upon the known
existence conditions and constructions, and compile known existence results for
small parameters. Some interesting quantum codes are constructed to demonstrate
their value.Comment: 33 pages including appendi
Improvements on non-equilibrium and transport Green function techniques: the next-generation transiesta
We present novel methods implemented within the non-equilibrium Green
function code (NEGF) transiesta based on density functional theory (DFT). Our
flexible, next-generation DFT-NEGF code handles devices with one or multiple
electrodes () with individual chemical potentials and electronic
temperatures. We describe its novel methods for electrostatic gating, contour
opti- mizations, and assertion of charge conservation, as well as the newly
implemented algorithms for optimized and scalable matrix inversion,
performance-critical pivoting, and hybrid parallellization. Additionally, a
generic NEGF post-processing code (tbtrans/phtrans) for electron and phonon
transport is presented with several novelties such as Hamiltonian
interpolations, electrode capability, bond-currents, generalized
interface for user-defined tight-binding transport, transmission projection
using eigenstates of a projected Hamiltonian, and fast inversion algorithms for
large-scale simulations easily exceeding atoms on workstation computers.
The new features of both codes are demonstrated and bench-marked for relevant
test systems.Comment: 24 pages, 19 figure
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