5,706 research outputs found
Quantum Codes from Generalized Reed-Solomon Codes and Matrix-Product Codes
One of the central tasks in quantum error-correction is to construct quantum
codes that have good parameters. In this paper, we construct three new classes
of quantum MDS codes from classical Hermitian self-orthogonal generalized
Reed-Solomon codes. We also present some classes of quantum codes from
matrix-product codes. It turns out that many of our quantum codes are new in
the sense that the parameters of quantum codes cannot be obtained from all
previous constructions
Quantum Block and Synchronizable Codes Derived from Certain Classes of Polynomials
One central theme in quantum error-correction is to construct quantum codes
that have a large minimum distance. In this paper, we first present a
construction of classical codes based on certain class of polynomials. Through
these classical codes, we are able to obtain some new quantum codes. It turns
out that some of quantum codes exhibited here have better parameters than the
ones available in the literature. Meanwhile, we give a new class of quantum
synchronizable codes with highest possible tolerance against misalignment from
duadic codes.Comment: 9 pages. arXiv admin note: text overlap with arXiv:1403.6192,
arXiv:1311.3416 by other author
Some New Results on the Cross Correlation of -sequences
The determination of the cross correlation between an -sequence and its
decimated sequence has been a long-standing research problem. Considering a
ternary -sequence of period , we determine the cross correlation
distribution for decimations and , where .
Meanwhile, for a binary -sequence of period , we make an initial
investigation for the decimation , where is even and . It is shown that the cross correlation
takes at least four values. Furthermore, we confirm the validity of two famous
conjectures due to Sarwate et al. and Helleseth in this case
Some new results on permutation polynomials over finite fields
Permutation polynomials over finite fields constitute an active research area
and have applications in many areas of science and engineering. In this paper,
four classes of monomial complete permutation polynomials and one class of
trinomial complete permutation polynomials are presented, one of which confirms
a conjecture proposed by Wu et al. (Sci. China Math., to appear. Doi:
10.1007/s11425-014-4964-2). Furthermore, we give two classes of trinomial
permutation polynomials, and make some progress on a conjecture about the
differential uniformity of power permutation polynomials proposed by Blondeau
et al. (Int. J. Inf. Coding Theory, 2010, 1, pp. 149-170).Comment: 21 pages. We have changed the title of our pape
Parallel Data Augmentation for Formality Style Transfer
The main barrier to progress in the task of Formality Style Transfer is the
inadequacy of training data. In this paper, we study how to augment parallel
data and propose novel and simple data augmentation methods for this task to
obtain useful sentence pairs with easily accessible models and systems.
Experiments demonstrate that our augmented parallel data largely helps improve
formality style transfer when it is used to pre-train the model, leading to the
state-of-the-art results in the GYAFC benchmark dataset.Comment: Accepted by ACL 2020. arXiv admin note: text overlap with
arXiv:1909.0600
On the Weight Distribution of Cyclic Codes with Niho Exponents
Recently, there has been intensive research on the weight distributions of
cyclic codes. In this paper, we compute the weight distributions of three
classes of cyclic codes with Niho exponents. More specifically, we obtain two
classes of binary three-weight and four-weight cyclic codes and a class of
nonbinary four-weight cyclic codes. The weight distributions follow from the
determination of value distributions of certain exponential sums. Several
examples are presented to show that some of our codes are optimal and some have
the best known parameters
New constructions of quantum MDS convolutional codes derived from generalized Reed-Solomon codes
Quantum convolutional codes can be used to protect a sequence of qubits of
arbitrary length against decoherence. In this paper, we give two new
constructions of quantum MDS convolutional codes derived from generalized
Reed-Solomon codes and obtain eighteen new classes of quantum MDS convolutional
codes. Most of them are new in the sense that the parameters of the codes are
different from all the previously known ones.Comment: arXiv admin note: text overlap with arXiv:1408.5782 by other author
Constructions of Strongly Regular Cayley Graphs Using Index Four Gauss Sums
We give a construction of strongly regular Cayley graphs on finite fields
\F_q by using union of cyclotomic classes and index 4 Gauss sums. In
particular, we obtain two infinite families of strongly regular graphs with new
parameters.Comment: 19 pages; to appear in Journal of Algebraic Combinatoric
The Dirichlet Problem of Fully Nonlinear Equations on Hermitian Manifolds
We study the Dirichlet problem of a class of fully nonlinear elliptic
equations on Hermitian manifolds and derive a priori estimates which
depend on the initial data on manifolds, the admissible subsolutions and the
upper bound of the gradients of the solutions. In some special cases, we obtain
the gradient estimates, and hence we can solve the corresponding Dirichlet
problem with admissible subsolutions. We also study the Hessian quotient
equations and -Hessian quotient equations on compact Hermitian
manifolds without boundary.Comment: 45 page
New pseudo-planar binomials in characteristic two and related schemes
Planar functions in odd characteristic were introduced by Dembowski and
Ostrom in order to construct finite projective planes in 1968. They were also
used in the constructions of DES-like iterated ciphers, error-correcting codes,
and signal sets. Recently, a new notion of pseudo-planar functions in even
characteristic was proposed by Zhou. These new pseudo-planar functions, as an
analogue of planar functions in odd characteristic, also bring about finite
projective planes. There are three known infinite families of pseudo-planar
monomial functions constructed by Schmidt and Zhou, and Scherr and Zieve. In
this paper, three new classes of pseudo-planar binomials are provided.
Moreover, we find that each pseudo-planar function gives an association scheme
which is defined on a Galois ring.Comment: Replaced the term "planar" with "pseudo-planar"; revised argument in
section
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