18,934 research outputs found
The Perfect Binary One-Error-Correcting Codes of Length 15: Part II--Properties
A complete classification of the perfect binary one-error-correcting codes of
length 15 as well as their extensions of length 16 was recently carried out in
[P. R. J. \"Osterg{\aa}rd and O. Pottonen, "The perfect binary
one-error-correcting codes of length 15: Part I--Classification," IEEE Trans.
Inform. Theory vol. 55, pp. 4657--4660, 2009]. In the current accompanying
work, the classified codes are studied in great detail, and their main
properties are tabulated. The results include the fact that 33 of the 80
Steiner triple systems of order 15 occur in such codes. Further understanding
is gained on full-rank codes via switching, as it turns out that all but two
full-rank codes can be obtained through a series of such transformations from
the Hamming code. Other topics studied include (non)systematic codes, embedded
one-error-correcting codes, and defining sets of codes. A classification of
certain mixed perfect codes is also obtained.Comment: v2: fixed two errors (extension of nonsystematic codes, table of
coordinates fixed by symmetries of codes), added and extended many other
result
Near MDS poset codes and distributions
We study -ary codes with distance defined by a partial order of the
coordinates of the codewords. Maximum Distance Separable (MDS) codes in the
poset metric have been studied in a number of earlier works. We consider codes
that are close to MDS codes by the value of their minimum distance. For such
codes, we determine their weight distribution, and in the particular case of
the "ordered metric" characterize distributions of points in the unit cube
defined by the codes. We also give some constructions of codes in the ordered
Hamming space.Comment: 13 pages, 1 figur
Fast Exact Search in Hamming Space with Multi-Index Hashing
There is growing interest in representing image data and feature descriptors
using compact binary codes for fast near neighbor search. Although binary codes
are motivated by their use as direct indices (addresses) into a hash table,
codes longer than 32 bits are not being used as such, as it was thought to be
ineffective. We introduce a rigorous way to build multiple hash tables on
binary code substrings that enables exact k-nearest neighbor search in Hamming
space. The approach is storage efficient and straightforward to implement.
Theoretical analysis shows that the algorithm exhibits sub-linear run-time
behavior for uniformly distributed codes. Empirical results show dramatic
speedups over a linear scan baseline for datasets of up to one billion codes of
64, 128, or 256 bits
Metric Learning for Temporal Sequence Alignment
In this paper, we propose to learn a Mahalanobis distance to perform
alignment of multivariate time series. The learning examples for this task are
time series for which the true alignment is known. We cast the alignment
problem as a structured prediction task, and propose realistic losses between
alignments for which the optimization is tractable. We provide experiments on
real data in the audio to audio context, where we show that the learning of a
similarity measure leads to improvements in the performance of the alignment
task. We also propose to use this metric learning framework to perform feature
selection and, from basic audio features, build a combination of these with
better performance for the alignment
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