52 research outputs found
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
Constructions of Good Entanglement-Assisted Quantum Error Correcting Codes
Entanglement-assisted quantum error correcting codes (EAQECCs) are a simple
and fundamental class of codes. They allow for the construction of quantum
codes from classical codes by relaxing the duality condition and using
pre-shared entanglement between the sender and receiver. However, in general it
is not easy to determine the number of shared pairs required to construct an
EAQECC. In this paper, we show that this number is related to the hull of the
classical code. Using this fact, we give methods to construct EAQECCs requiring
desirable amount of entanglement. This leads to design families of EAQECCs with
good error performance. Moreover, we construct maximal entanglement EAQECCs
from LCD codes. Finally, we prove the existence of asymptotically good EAQECCs
in the odd characteristic case
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
Entanglement-assisted quantum codes from Galois LCD codes
Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of
preexisting entanglement between the sender and receiver to boost the rate of
transmission. It is possible to construct an EAQECC from any classical linear
code, unlike standard quantum error-correcting codes, which can only be
constructed from dual-containing codes. However, the parameter of ebits is
usually calculated by computer search. In this paper, we construct four classes
of MDS entanglement-assisted quantum error-correcting codes (MDS EAQECCs) based
on -Galois LCD MDS codes for some certain code lengths, where the parameter
of ebits can be easily generated algebraically and not by computational
search. Moreover, the constructed four classes of EAQECCs are also
maximal-entanglement EAQECCs
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
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
On Classical and Quantum MDS-Convolutional BCH Codes
Several new families of multi-memory classical convolutional
Bose-Chaudhuri-Hocquenghem (BCH) codes as well as families of unit-memory
quantum convolutional codes are constructed in this paper. Our unit-memory
classical and quantum convolutional codes are optimal in the sense that they
attain the classical (quantum) generalized Singleton bound. The constructions
presented in this paper are performed algebraically and not by computational
search.Comment: Accepted for publication in IEEE-Transactions on Information Theor
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
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
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
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