6,979 research outputs found
New Constant-Weight Codes from Propagation Rules
This paper proposes some simple propagation rules which give rise to new
binary constant-weight codes.Comment: 4 page
Transitive and self-dual codes attaining the Tsfasman-Vladut-Zink bound
A major problem in coding theory is the question of whether the class of cyclic codes is asymptotically good. In this correspondence-as a generalization of cyclic codes-the notion of transitive codes is introduced (see Definition 1.4 in Section I), and it is shown that the class of transitive codes is asymptotically good. Even more, transitive codes attain the Tsfasman-Vladut-Zink bound over F-q, for all squares q = l(2). It is also shown that self-orthogonal and self-dual codes attain the Tsfasman-Vladut-Zink bound, thus improving previous results about self-dual codes attaining the Gilbert-Varshamov bound. The main tool is a new asymptotically optimal tower E-0 subset of E-1 subset of E-2 subset of center dot center dot center dot of function fields over F-q (with q = l(2)), where all extensions E-n/E-0 are Galois
Codes for Key Generation in Quantum Cryptography
As an alternative to the usual key generation by two-way communication in
schemes for quantum cryptography, we consider codes for key generation by
one-way communication. We study codes that could be applied to the raw key
sequences that are ideally obtained in recently proposed scenarios for quantum
key distribution, which can be regarded as communication through symmetric
four-letter channels.Comment: IJQI format, 13 pages, 1 tabl
Improved asymptotic bounds for codes using distinguished divisors of global function fields
For a prime power , let be the standard function in the
asymptotic theory of codes, that is, is the largest
asymptotic information rate that can be achieved for a given asymptotic
relative minimum distance of -ary codes. In recent years the
Tsfasman-Vl\u{a}du\c{t}-Zink lower bound on was improved by
Elkies, Xing, and Niederreiter and \"Ozbudak. In this paper we show further
improvements on these bounds by using distinguished divisors of global function
fields. We also show improved lower bounds on the corresponding function
for linear codes
A Survey on Metric Learning for Feature Vectors and Structured Data
The need for appropriate ways to measure the distance or similarity between
data is ubiquitous in machine learning, pattern recognition and data mining,
but handcrafting such good metrics for specific problems is generally
difficult. This has led to the emergence of metric learning, which aims at
automatically learning a metric from data and has attracted a lot of interest
in machine learning and related fields for the past ten years. This survey
paper proposes a systematic review of the metric learning literature,
highlighting the pros and cons of each approach. We pay particular attention to
Mahalanobis distance metric learning, a well-studied and successful framework,
but additionally present a wide range of methods that have recently emerged as
powerful alternatives, including nonlinear metric learning, similarity learning
and local metric learning. Recent trends and extensions, such as
semi-supervised metric learning, metric learning for histogram data and the
derivation of generalization guarantees, are also covered. Finally, this survey
addresses metric learning for structured data, in particular edit distance
learning, and attempts to give an overview of the remaining challenges in
metric learning for the years to come.Comment: Technical report, 59 pages. Changes in v2: fixed typos and improved
presentation. Changes in v3: fixed typos. Changes in v4: fixed typos and new
method
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