7,726 research outputs found
Subspace subcodes of Reed-Solomon codes
We introduce a class of nonlinear cyclic error-correcting codes, which we call subspace subcodes of Reed-Solomon (SSRS) codes. An SSRS code is a subset of a parent Reed-Solomon (RS) code consisting of the RS codewords whose components all lie in a fixed ν-dimensional vector subspace S of GF (2m). SSRS codes are constructed using properties of the Galois field GF(2m). They are not linear over the field GF(2ν), which does not come into play, but rather are Abelian group codes over S. However, they are linear over GF(2), and the symbol-wise cyclic shift of any codeword is also a codeword. Our main result is an explicit but complicated formula for the dimension of an SSRS code. It implies a simple lower bound, which gives the true value of the dimension for most, though not all, subspaces. We also prove several important duality properties. We present some numerical examples, which show, among other things, that (1) SSRS codes can have a higher dimension than comparable subfield subcodes of RS codes, so that even if GF(2ν) is a subfield of GF(2m), it may not be the best ν-dimensional subspace for constructing SSRS codes; and (2) many high-rate SSRS codes have a larger dimension than any previously known code with the same values of n, d, and q, including algebraic-geometry codes. These examples suggest that high-rate SSRS codes are promising candidates to replace Reed-Solomon codes in high-performance transmission and storage systems
Gravitational Lensing in Clusters of Galaxies
Gravitational lensing in clusters of galaxies is an efficient tool to probe
the mass distribution of galaxies and clusters, high redshift objects thanks to
the gravitational amplification, and the geometry of the universe. We review
some important aspects of cluster lensing and related issues in observational
cosmology.Comment: invited review of the journal: Progress of Theoretical Physics (in
press) 51 pages - 33 figure
A possible route to spontaneous reduction of the heat conductivity by a temperature gradient driven instability in electron-ion plasmas
We have shown that there exists low-frequency growing modes driven by a
global temperature gradient in electron and ion plasmas, by linear perturbation
analysis within the frame work of plasma Kinetic theory. The driving force of
the instability is the local deviation of the distribution function from the
Maxwell-Boltzmann due to global temperature gradient. Application to the
intracluster medium shows that scattering of the particles due to waves excited
by the instability is possible to reduce mean free paths of electron and ion
down to five to seven order of magnitude than the mean free paths due to
Coulomb collisions. This may provide a hint to explain why hot and cool gas can
co-exist in the intracluster medium in spite of the very short evaporation time
scale due to thermal conduction if the conductivity is the classical Spitzer
value. Our results suggest that the realization of the global thermal
equilibrium is postponed by the local instability which is induced for quicker
realization of local thermal equilibrium state in plasmas. The instability
provides a new possibility to create and grow cosmic magnetic fields without
any seed magnetic field.Comment: Accepted for publication in ApJ: 16 pages, 1figur
Spectroscopic confirmation of a cluster of galaxies at z=1 in the field of the gravitational lens MG2016+112
We present new optical data on the cluster AX J2019+1127 identified by the
X-ray satellite ASCA at z\sim 1 (Hattori et al. 1997). The data suggest the
presence of a high-redshift cluster of galaxies responsible for the large
separation triple quasar MG2016+112. Our deep photometry reveals an excess of
z\sim 1 galaxy candidates, as already suspected by Benitez et al. (1999). Our
spectroscopic survey of 44 objects in the field shows an excess of 6 red
galaxies securely identified at z \sim 1, with a mean redshift of z =1.005 +/-
0.002. We estimate a velocity dispersion of \sigma = 771 (+430/-160) km s(-1)
based on these 6 galaxies and a V-band mass-to-light ratio of 215 (+308/-77)
h_50 M/L_sol. Our observations thus confirm the existence of a massive
structure acting as the lens, which explains the unusual configuration of the
triple quasar. Hence, there is no more need to invoke the existence of a ``dark
cluster'' to understand this lens system.Comment: 8 pages, 4 figures, uses aa.cls, accepted to Astronomy and
Astrophysics with minor change
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