375 research outputs found
The completion of optimal -packings
A 3- packing design consists of an -element set and a
collection of -element subsets of , called {\it blocks}, such that every
-element subset of is contained in at most one block. The packing number
of quadruples denotes the number of blocks in a maximum
- packing design, which is also the maximum number of
codewords in a code of length , constant weight , and minimum Hamming
distance 4. In this paper the undecided 21 packing numbers are shown
to be equal to Johnson bound
where ,
is odd,
List Decodability at Small Radii
, the smallest for which every binary error-correcting code
of length and minimum distance is decodable with a list of size
up to radius , is determined for all . As a result,
is determined for all , except for 42 values of .Comment: to appear in Designs, Codes, and Cryptography (accepted October 2010
An Analysis of Thickness-shear Vibrations of an Annular Plate with the Mindlin Plate Equations
The Mindlin plate equations with the consideration of thickness-shear
deformation as an independent variable have been used for the analysis of
vibrations of quartz crystal resonators of both rectangular and circular types.
The Mindlin or Lee plate theories that treat thickness-shear deformation as an
independent higher-order vibration mode in a coupled system of two-dimensional
variables are the choice of theory for analysis. For circular plates, we
derived the Mindlin plate equations in a systematic manner as demonstrated by
Mindlin and others and obtained the truncated two-dimensional equations of
closely coupled modes in polar coordinates. We simplified the equations for
vibration modes in the vicinity of fundamental thickness-shear frequency and
validated the equations and method. To explore newer structures of quartz
crystal resonators, we utilized the Mindlin plate equations for the analysis of
annular plates with fixed inner and free outer edges for frequency spectra. The
detailed analysis of vibrations of circular plates for the normalized frequency
versus dimensional parameters provide references for optimal selection of
parameters based on the principle of strong thickness-shear mode and minimal
presence of other modes to enhance energy trapping through maintaining the
strong and pure thickness-shear vibrations insensitive to some complication
factors such as thermal and initial stresses.Comment: Paper to be presented to the 2015 IEEE International Frequency
Control Symposium and European Frequency and Time Forum, Denver, CO, USA.
April 12-16, 201
Maximum Distance Separable Codes for Symbol-Pair Read Channels
We study (symbol-pair) codes for symbol-pair read channels introduced
recently by Cassuto and Blaum (2010). A Singleton-type bound on symbol-pair
codes is established and infinite families of optimal symbol-pair codes are
constructed. These codes are maximum distance separable (MDS) in the sense that
they meet the Singleton-type bound. In contrast to classical codes, where all
known q-ary MDS codes have length O(q), we show that q-ary MDS symbol-pair
codes can have length \Omega(q^2). In addition, we completely determine the
existence of MDS symbol-pair codes for certain parameters
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