30 research outputs found
Entanglement-assisted quantum MDS codes from constacyclic codes with large minimum distance
The entanglement-assisted (EA) formalism allows arbitrary classical linear
codes to transform into entanglement-assisted quantum error correcting codes
(EAQECCs) by using pre-shared entanglement between the sender and the receiver.
In this work, we propose a decomposition of the defining set of constacyclic
codes. Using this method, we construct four classes of -ary
entanglement-assisted quantum MDS (EAQMDS) codes based on classical
constacyclic MDS codes by exploiting less pre-shared maximally entangled
states. We show that a class of -ary EAQMDS have minimum distance upper
limit greater than . Some of them have much larger minimum distance than
the known quantum MDS (QMDS) codes of the same length. Most of these -ary
EAQMDS codes are new in the sense that their parameters are not covered by the
codes available in the literature
Constructions of q-ary entanglement-assisted quantum MDS codes with minimum distance greater than q + 1
The entanglement-assisted stabilizer formalism provides a useful framework
for constructing quantum error-correcting codes (QECC), which can transform
arbitrary classical linear codes into entanglement-assisted quantum error
correcting codes (EAQECCs) by using pre-shared entanglement between the sender
and the receiver. In this paper, we construct five classes of
entanglement-assisted quantum MDS (EAQMDS) codes based on classical MDS codes
by exploiting one or more pre-shared maximally entangled states. We show that
these EAQMDS codes have much larger minimum distance than the standard quantum
MDS (QMDS) codes of the same length, and three classes of these EAQMDS codes
consume only one pair of maximally entangled states.Comment: 12 page
New entanglement-assisted MDS quantum codes from constacyclic codes
Construction of good quantum codes via classical codes is an important task
for quantum information and quantum computing. In this work, by virtue of a
decomposition of the defining set of constacyclic codes we have constructed
eight new classes of entanglement-assisted quantum maximum distance separable
codes
Two families of Entanglement-assisted quantum MDS codes from constacyclic codes
Entanglement-assisted quantum error correcting codes (EAQECCs) can be derived
from arbitrary classical linear codes. However, it is a very difficult task to
determine the number of entangled states required. In this work, using the
method of the decomposition of the defining set of constacyclic codes, we
construct two families of q-ary entanglement-assisted quantum MDS (EAQMDS)
codes based on classical constacyclic MDS codes by exploiting less pre-shared
maximally entangled states. We show that a class of q-ary EAQMDS have minimum
distance upper bound greater than q. Some of them have much larger minimum
distance than the known quantum MDS (QMDS) codes of the same length. Most of
these q-ary EAQMDS codes are new in the sense that their parameters are not
covered by the codes available in the literature
Two families of Entanglement-assisted Quantum MDS Codes from cyclic Codes
With entanglement-assisted (EA) formalism, arbitrary classical linear codes
are allowed to transform into EAQECCs by using pre-shared entanglement between
the sender and the receiver. In this paper, based on classical cyclic MDS codes
by exploiting pre-shared maximally entangled states, we construct two families
of -ary entanglement-assisted quantum MDS codes
, where q is a prime
power in the form of , and or . We show
that all of -ary EAQMDS have minimum distance upper limit much larger than
the known quantum MDS (QMDS) codes of the same length. Most of these -ary
EAQMDS codes are new in the sense that their parameters are not covered by the
codes available in the literature.Comment: arXiv admin note: substantial text overlap with arXiv:1803.04168,
arXiv:1912.1203
New Classes of Entanglement-assisted Quantum MDS Codes
In this paper, we produce two new classes of entanglement-assisted quantum
MDS codes (EAQMDS codes) with length and via cyclic codes
over finite fields of odd characteristic. Among our constructions there are
many EAQMDS codes with new parameters which have never been reported. And some
of them have great larger minimum distance than known results.Comment: 10 page
Entanglement-assisted Quantum Codes from Cyclic Codes
Entanglement-assisted quantum (QUENTA) codes are a subclass of quantum
error-correcting codes which use entanglement as a resource. These codes can
provide error correction capability higher than the codes derived from the
traditional stabilizer formalism. In this paper, it is shown a general method
to construct QUENTA codes from cyclic codes. Afterwards, the method is applied
to Reed-Solomon codes, BCH codes, and general cyclic codes. We use the
Euclidean and Hermitian construction of QUENTA codes. Two families of QUENTA
codes are maximal distance separable (MDS), and one is almost MDS or almost
near MDS. The comparison of the codes in this paper is mostly based on the
quantum Singleton bound
Cyclic codes and some new entanglement-assisted quantum MDS codes
Entanglement-assisted quantum error correcting codes (EAQECCs) play a
significant role in protecting quantum information from decoherence and quantum
noise. Recently, constructing entanglement-assisted quantum maximum distance
separable (EAQMDS) codes with flexible parameters has received much attention.
In this work, four families of EAQMDS codes with a more general length are
presented. And the method of selecting defining set is different from others.
Compared with all the previously known results, the EAQMDS codes we constructed
have larger minimum distance. All of these EAQMDS codes are new in the sense
that their parameters are not covered by the quantum codes available in the
literature
A new method for constructing EAQEC MDS codes
Entanglement-assisted quantum error-correcting (EAQEC) codes make use of
preexisting entanglement between the sender and receiver to boost the rate of
transmission. It is possible to construct an EAQEC code from any classical
linear code, unlike standard quantum error-correcting codes, which can only be
constructed from dual-containing codes. However, the number of pre-shared
maximally entangled states is usually calculated by computer search. In this
paper, we first give a new formula for calculating the number of pre-shared
maximally entangled states. Then, using this formula, we construct three
classes of new entanglement-assisted quantum error-correcting
maximum-distance-separable ( EAQEC MDS) codes.Comment: 16 pages,3 table
New entanglement-assisted quantum MDS codes with length
The entanglement-assisted stabilizer formalism can transform arbitrary
classical linear codes into entanglement-assisted quantum error correcting
codes (EAQECCs). In this work, we construct some new entanglement-assisted
quantum MDS (EAQMDS) codes with length from cyclic codes.
Compared with all the previously known parameters with the same length, all of
them have flexible parameters and larger minimum distance