49,119 research outputs found
Asymptotic bounds for spherical codes
The set of all error-correcting codes C over a fixed finite alphabet F of
cardinality q determines the set of code points in the unit square with
coordinates (R(C), delta (C)):= (relative transmission rate, relative minimal
distance). The central problem of the theory of such codes consists in
maximizing simultaneously the transmission rate of the code and the relative
minimum Hamming distance between two different code words. The classical
approach to this problem explored in vast literature consists in the inventing
explicit constructions of "good codes" and comparing new classes of codes with
earlier ones. Less classical approach studies the geometry of the whole set of
code points (R,delta) (with q fixed), at first independently of its
computability properties, and only afterwords turning to the problems of
computability, analogies with statistical physics etc. The main purpose of this
article consists in extending this latter strategy to domain of spherical
codes.Comment: 34 pages amstex, 3 figure
Rigidity of spherical codes
A packing of spherical caps on the surface of a sphere (that is, a spherical
code) is called rigid or jammed if it is isolated within the space of packings.
In other words, aside from applying a global isometry, the packing cannot be
deformed. In this paper, we systematically study the rigidity of spherical
codes, particularly kissing configurations. One surprise is that the kissing
configuration of the Coxeter-Todd lattice is not jammed, despite being locally
jammed (each individual cap is held in place if its neighbors are fixed); in
this respect, the Coxeter-Todd lattice is analogous to the face-centered cubic
lattice in three dimensions. By contrast, we find that many other packings have
jammed kissing configurations, including the Barnes-Wall lattice and all of the
best kissing configurations known in four through twelve dimensions. Jamming
seems to become much less common for large kissing configurations in higher
dimensions, and in particular it fails for the best kissing configurations
known in 25 through 31 dimensions. Motivated by this phenomenon, we find new
kissing configurations in these dimensions, which improve on the records set in
1982 by the laminated lattices.Comment: 39 pages, 8 figure
The weight distribution and randomness of linear codes
Finding the weight distributions of block codes is a problem of theoretical and practical interest. Yet the weight distributions of most block codes are still unknown except for a few classes of block codes. Here, by using the inclusion and exclusion principle, an explicit formula is derived which enumerates the complete weight distribution of an (n,k,d) linear code using a partially known weight distribution. This expression is analogous to the Pless power-moment identities - a system of equations relating the weight distribution of a linear code to the weight distribution of its dual code. Also, an approximate formula for the weight distribution of most linear (n,k,d) codes is derived. It is shown that for a given linear (n,k,d) code over GF(q), the ratio of the number of codewords of weight u to the number of words of weight u approaches the constant Q = q(-)(n-k) as u becomes large. A relationship between the randomness of a linear block code and the minimum distance of its dual code is given, and it is shown that most linear block codes with rigid algebraic and combinatorial structure also display certain random properties which make them similar to random codes with no structure at all
SiSeRHMap v1.0: A simulator for mapped seismic response using a hybrid model
SiSeRHMap is a computerized methodology capable of drawing up prediction maps of
seismic response. It was realized on the basis of a hybrid model which combines different
approaches and models in a new and non-conventional way. These approaches
5 and models are organized in a code-architecture composed of five interdependent
modules. A GIS (Geographic Information System) Cubic Model (GCM), which is a layered
computational structure based on the concept of lithodynamic units and zones,
aims at reproducing a parameterized layered subsoil model. A metamodeling process
confers a hybrid nature to the methodology. In this process, the one-dimensional linear
10 equivalent analysis produces acceleration response spectra of shear wave velocitythickness
profiles, defined as trainers, which are randomly selected in each zone. Subsequently,
a numerical adaptive simulation model (Spectra) is optimized on the above
trainer acceleration response spectra by means of a dedicated Evolutionary Algorithm
(EA) and the Levenberg–Marquardt Algorithm (LMA) as the final optimizer. In the fi15
nal step, the GCM Maps Executor module produces a serial map-set of a stratigraphic
seismic response at different periods, grid-solving the calibrated Spectra model. In addition,
the spectra topographic amplification is also computed by means of a numerical
prediction model. This latter is built to match the results of the numerical simulations
related to isolate reliefs using GIS topographic attributes. In this way, different sets
20 of seismic response maps are developed, on which, also maps of seismic design response
spectra are defined by means of an enveloping technique
Implicit solutions with consistent additive and multiplicative components
Use of multiple-point-constraint
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