36,743 research outputs found
A Family of Binary Sequences with Optimal Correlation Property and Large Linear Span
A family of binary sequences is presented and proved to have optimal
correlation property and large linear span. It includes the small set of Kasami
sequences, No sequence set and TN sequence set as special cases. An explicit
lower bound expression on the linear span of sequences in the family is given.
With suitable choices of parameters, it is proved that the family has
exponentially larger linear spans than both No sequences and TN sequences. A
class of ideal autocorrelation sequences is also constructed and proved to have
large linear span.Comment: 21 page
Characterizing finite-dimensional quantum behavior
We study and extend the semidefinite programming (SDP) hierarchies introduced
in [Phys. Rev. Lett. 115, 020501] for the characterization of the statistical
correlations arising from finite dimensional quantum systems. First, we
introduce the dimension-constrained noncommutative polynomial optimization
(NPO) paradigm, where a number of polynomial inequalities are defined and
optimization is conducted over all feasible operator representations of bounded
dimensionality. Important problems in device independent and semi-device
independent quantum information science can be formulated (or almost
formulated) in this framework. We present effective SDP hierarchies to attack
the general dimension-constrained NPO problem (and related ones) and prove
their asymptotic convergence. To illustrate the power of these relaxations, we
use them to derive new dimension witnesses for temporal and Bell-type
correlation scenarios, and also to bound the probability of success of quantum
random access codes.Comment: 17 page
Full-length non-linear binary sequences with Zero Correlation Zone for multiuser communications
none3noThe research on new sets of sequences that can be applied as spreading codes in multiple user communications is still an active area, even if this topic has been extensively investigated since long time. In fact, new communication paradigms like dense and decentralized wireless networks, where there is no central controller to assign the resources to the nodes, are revamping the interest on finding large sets of sequences providing adequate correlation properties to support a big number of nodes, in potentially hostile channels. This paper focuses on the Zero Correlation Zone (ZCZ) property exhibited by a family of nonlinear binary sequences featuring a great cardinality of their set, and good security-related features, and provides evidence of their suitability to multiuser communications, in channels affected by multipath.Sarayloo, M.; Gambi, E.; Spinsante, S.Sarayloo, Mahdiyar; Gambi, Ennio; Spinsante, Susann
On the List-Decodability of Random Linear Codes
For every fixed finite field \F_q, and , we
prove that with high probability a random subspace of \F_q^n of dimension
has the property that every Hamming ball of radius
has at most codewords.
This answers a basic open question concerning the list-decodability of linear
codes, showing that a list size of suffices to have rate within
of the "capacity" . Our result matches up to constant
factors the list-size achieved by general random codes, and gives an
exponential improvement over the best previously known list-size bound of
.
The main technical ingredient in our proof is a strong upper bound on the
probability that random vectors chosen from a Hamming ball centered at
the origin have too many (more than ) vectors from their linear
span also belong to the ball.Comment: 15 page
Full-length non-linear binary sequences with Zero Correlation Zone for multiuser communications
The research on new sets of sequences to be used asspreading codes in multiple user communications is still an activearea, despite the great amount of literature available since manyyears on this topic. In fact, new paradigms like dense anddecentralized wireless networks, where there is no centralcontroller to assign the resources to the nodes, are revamping theinterest on large sets of sequences providing adequate correlationproperties to support a big number of nodes, in potentially hostilechannels. This paper focuses on the Zero Correlation Zone (ZCZ)property exhibited by a family of non-linear binary sequencesfeaturing a great cardinality of their set and good securityrelatedfeatures, and provides evidence of their suitability tomultiuser communications, in channels affected by multipath
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