125 research outputs found
A new method for constructing small-bias spaces from Hermitian codes
We propose a new method for constructing small-bias spaces through a
combination of Hermitian codes. For a class of parameters our multisets are
much faster to construct than what can be achieved by use of the traditional
algebraic geometric code construction. So, if speed is important, our
construction is competitive with all other known constructions in that region.
And if speed is not a matter of interest the small-bias spaces of the present
paper still perform better than the ones related to norm-trace codes reported
in [12]
ON THE ORDER BOUNDS FOR ONE-POINT AG CODES
The order bound for the minimum distance of algebraic geometry codes was originally defined for the duals of one-point codes and later generalized for arbitrary algebraic geometry codes. Another bound of order type for the minimum distance of general linear codes, and for codes from order domains in particular, was given in [1]. Here we investigate in detail the application of that bound to one-point algebraic geometry codes, obtaining a bound d* for the minimum distance of these codes. We establish a connection between d* and the order bound and its generalizations. We also study the improved code constructions based on d*. Finally we extend d* to all generalized Hamming weights.53489504Danish National Science Research Council [FNV-21040368]Danish FNU [272-07-0266]Junta de CyL [VA065A07]Spanish Ministry for Science and Technology [MTM-2007-66842-C02-01, MTM 2007-64704]Aalborg UniversityThe Technical University of DenmarkDanish National Science Research Council [FNV-21040368]Danish FNU [272-07-0266]Junta de CyL [VA065A07]Spanish Ministry for Science and Technology [MTM-2007-66842-C02-01, MTM 2007-64704
Bounding the number of points on a curve using a generalization of Weierstrass semigroups
In this article we use techniques from coding theory to derive upper bounds
for the number of rational places of the function field of an algebraic curve
defined over a finite field. The used techniques yield upper bounds if the
(generalized) Weierstrass semigroup [P. Beelen, N. Tuta\c{s}: A generalization
of the Weierstrass semigroup, J. Pure Appl. Algebra, 207(2), 2006] for an
-tuple of places is known, even if the exact defining equation of the curve
is not known. As shown in examples, this sometimes enables one to get an upper
bound for the number of rational places for families of function fields. Our
results extend results in [O. Geil, R. Matsumoto: Bounding the number of
-rational places in algebraic function fields using Weierstrass
semigroups. Pure Appl. Algebra, 213(6), 2009]
Relative generalized hamming weights and extended weight polynomials of almost affine codes
This is a post-peer-review, pre-copyedit version of an article published in Lecture Notes in Computer Science, International Castle Meeting on Coding Theory and Applications ICMCTA 2017: Coding Theory and Applications, 207-216. The final authenticated version is available online at: http://dx.doi.org/10.1007/978-3-319-66278-7_17 .This paper is devoted to giving a generalization from linear
codes to the larger class of almost affine codes of two different results.
One such result is how one can express the relative generalized Hamming
weights of a pair of codes in terms of intersection properties between the
smallest of these codes and subcodes of the largest code. The other result
tells how one can find the extended weight polynomials, expressing the
number of codewords of each possible weight, for each code in an infinite
hierarchy of extensions of a code over a given alphabet. Our tools will
be demi-matroids and matroids
Selected-area small-angle electron diffraction
Selected-area electron diffraction capable of resolving spacings up to 2000 Å from first-order discrete reflections has been achieved using a standard, double-condenser electron microscope. The technique allows photographing of the selected area, at sufficient magnification, that gives rise to the small-angle scattering pattern, in addition to the normal capabilities of obtaining related wide-angle diffraction and wide-angle and small-angle dark-field micrographs. Most, but not all, of the results of discrete and diffuse, small-angle electron diffraction studies from a large variety of specimens including drawn, annealed polyethylene, latex particles, evaporated gold particles, grating replicas, and slit edges have been explained on the basis of the structures observed in the corresponding electron micrographs. Small-angle electron diffraction is found to be more sensitive to defects in the packing of the scattering centres than small-angle X-ray scattering.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44682/1/10853_2004_Article_BF00562952.pd
Imaging neutral hydrogen on large-scales during the Epoch of Reionization with LOFAR
The first generation of redshifted 21 cm detection experiments, carried out
with arrays like LOFAR, MWA and GMRT, will have a very low signal-to-noise
ratio per resolution element (\sim 0.2). In addition, whereas the variance of
the cosmological signal decreases on scales larger than the typical size of
ionization bubbles, the variance of the formidable galactic foregrounds
increases, making it hard to disentangle the two on such large scales. The poor
sensitivity on small scales on the one hand, and the foregrounds effect on
large scales on the other hand, make direct imaging of the Epoch of
Reionization of the Universe very difficult, and detection of the signal
therefore is expected to be statistical.Despite these hurdles, in this paper we
argue that for many reionization scenarios low resolution images could be
obtained from the expected data. This is because at the later stages of the
process one still finds very large pockets of neutral regions in the IGM,
reflecting the clustering of the large-scale structure, which stays strong up
to scales of \sim 120 comoving Mpc/h (\sim 1 degree). The coherence of the
emission on those scales allows us to reach sufficient S/N (\sim 3) so as to
obtain reionization 21 cm images. Such images will be extremely valuable for
answering many cosmological questions but above all they will be a very
powerful tool to test our control of the systematics in the data. The existence
of this typical scale (\sim 120 comoving Mpc/h) also argues for designing
future EoR experiments, e.g., with SKA, with a field of view of at least 4
degree.Comment: Replaced with final version (minor changes), 9 figures, 11 pages,
accepted for publication in MNRA
Polarization leakage in epoch of reionization windows – I. Low Frequency Array observations of the 3C196 field
Detection of the 21-cm signal coming from the epoch of reionization (EoR) is challenging especially because, even after removing the foregrounds, the residual Stokes I maps contain leakage from polarized emission that can mimic the signal. Here, we discuss the instrumental polarization of LOFAR and present realistic simulations of the leakages between Stokes parameters. From the LOFAR observations of polarized emission in the 3C196 field, we have quantified the level of polarization leakage caused by the nominal model beam of LOFAR, and compared it with the EoR signal using power spectrum analysis. We found that at 134– 166 MHz, within the central 4◦ of the field the (Q,U)→I leakage power is lower than the EoR signal at k<0.3 Mpc−¹. The leakage was found to be localized around a Faraday depth of 0, and the rms of the leakage as a fraction of the rms of the polarized emission was shown to vary between 0.2–0.3%, both of which could be utilized in the removal of leakage. Moreover, we could define an ‘EoR window’ in terms of the polarization leakage in the cylindrical power spectrum above the PSF-induced wedge and below k∥∼0.5 Mpc−¹, and the window extended up to k∥∼1 Mpc−¹ at all k⊥ when 70% of the leakage had been removed. These LOFAR results show that even a modest polarimetric calibration over a field of view of ≲4∘ in the future arrays like SKA will ensure that the polarization leakage remains well below the expected EoR signal at the scales of 0.02–1 Mpc−¹
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