New Entanglement-Assisted Quantum MDS Codes Derived From Generalized Reed-Solomon Codes

International Journal of Theoretical Physics - Entanglement-assisted quantum error-correcting codes (abbreviate to EAQECCs) expand the usual paradigm of quantum error correction by allowing two...     

Some Families of Asymmetric Quantum MDS Codes Constructed from Constacyclic Codes

Quantum maximal-distance-separable (MDS) codes that satisfy quantum Singleton bound with different lengths have been constructed by some researchers. In this paper, seven families of asymmetric quantum MDS codes are constructed by using constacyclic codes. We weaken the case of Hermitian-dual containing codes that can be applied to construct asymmetric quantum MDS codes with parameters \([[n,k,d_{z}/d_{x}]]_{q^{2}}\). These quantum codes are able to correct quantum errors with greater asymmetry. Moreover, these quantum codes constructed in this paper are different from the ones in the literature.     

Entanglement-Assisted Quantum Negacyclic BCH Codes

International Journal of Theoretical Physics - The entanglement-assisted quantum error correcting codes (EAQECCs) are a simple and important class of quantum codes. The entanglement-assisted...     

Quantum Codes Derived from Cyclic Codes

In this note, we present a construction of new nonbinary quantum codes with good parameters. These codes are obtained by applying the Calderbank-Shor-Steane (CSS) construction. In order to do this, we show the existence of (classical) cyclic codes whose defining set consists of only one cyclotomic coset containing at least two consecutive integers.     

New Quantum Codes Derived from Cyclic Codes

International Journal of Theoretical Physics - In this paper, we construct optimal or almost optimal dual-containing cyclic codes from cyclotomic classes of order r. Based on these cyclic codes...     

Some Families of Quantum BCH Codes

Classical Bose-Chaudhuri-Hocquenghem (BCH) codes over finite fields have been studied extensively. The Calderbank-Shor-Steane (CSS) construction, especially Steane’s enlargement, and Hermitian construction are the most widely used methods in design of quantum codes. The BCH codes containing their Euclidean dual or Hermitian dual codes can be used to generate good stabilizer codes. Therefore, we can construct quantum codes by classical BCH codes over finite fields in this paper. Firstly, we study the properties of such classical BCH codes in terms of the cyclotomic cosets. It is convenient to compute the dimension of new quantum BCH codes. Meanwhile, it ensures that classical BCH codes are Euclidean dual-containing or Hermitian dual-containing. These results about suitable cyclotomic cosets make it possible to construct several new families of nonbinary quantum BCH codes with a given parameter set. Compared with the ones available in the literature, the quantum BCH codes in our schemes have good parameters. In particular, we extend to more general cases than known results.

     

Some New Entanglement-Assisted Quantum Error-Correcting MDS Codes with Length q 2 + 1 13 $\frac {q^{2}+1}{13}$

International Journal of Theoretical Physics - Entanglement-assisted quantum maximum distance separable (MDS) codes form a significant class of quantum codes. By using constacyclic codes, we...     

Quantum Codes Derived from Negacyclic Codes

Recently, La Guardia constructed some new quantum codes from cyclic codes (La Guardia, Int. J. Theor. Phys., 2017). Inspired by this work, we consider quantum codes construction from negacyclic codes, not equivalent to cyclic codes, with only one cyclotomic coset containing at least two odd consecutive integers of even length. Some new quantum codes are obtained by this class of negacyclic codes.     

New Optimal Asymmetric Quantum Codes Derived from Negacyclic Codes

The construction of quantum maximum-distance-separable (MDS) codes have been studied by many researchers for many years. Here, by using negacyclic codes, we construct two families of asymmetric quantum codes. The first family is the asymmetric quantum codes with parameters $[[q^{2}+1,q^{2}+1-2(t+k+1),(2k+2)/(2t+2)]]_{q^{2}}$ , where 0≤t≤k≤(q?1)/2, $q \equiv1(\operatorname{mod} 4)$ , and k, t are positive integers. The second one is the asymmetric quantum codes with parameters $[[(q^{2}+1)/2,(q^{2}+1)/2-2(t+k),(2k+1)/(2t+1)]]_{q^{2}}$ , where 1≤t≤k≤(q?1)/2, and k, t are positive integers. Moreover, the constructed asymmetric quantum codes are optimal and different from the codes available in the literature.     

Construction of Binary Quantum Error-Correcting Codes from Orthogonal Array

By using difference schemes, orthogonal partitions and a replacement method, some new methods to construct pure quantum error-correcting codes are provided from orthogonal arrays. As an application of these methods, we construct several infinite series of quantum error-correcting codes including some optimal ones. Compared with the existing binary quantum codes, more new codes can be constructed, which have a lower number of terms (i.e., the number of computational basis states) for each of their basis states.     

A Construction of Quantum Error-Locating Codes

We present the construction of quantum error-locating(QEL) codes based on classical error-locating(EL)codes. Similar to classical EL codes, QEL codes lie midway between quantum error-correcting codes and quantum errordetecting codes. Then QEL codes can locate qubit errors within one sub-block of the received qubit symbols but do not need to determine the exact locations of the erroneous qubits. We show that, an e-error-locating code derived from an arbitrary binary cyclic code with generator polynomial g(x), can lead to a QEL code with e error-locating abilities, only if g(x) does not contain the(1 + x)-factor.     

New Quantum Codes from Skew Constacyclic Codes Over a Class Of Non-Chain Rings Re,q

International Journal of Theoretical Physics - In this paper, for q = pm (p is prime) such that q ≡ 1 (mod e), we study skew constacyclic codes over a class of non-chain rings...