Query: entanglement-assisted quantum MDS codes constacyclic codes

title: On pure MDS asymmetric entanglement assisted quantum error correcting codes
abstract: Recently, Galindo et al. introduced the concept of asymmetric entanglement assisted quantum error correcting codes (AEAQECCs) from CalderbankShor Steane (CSS) construction. In general, it's difficult to determine the required number of maximally entangled states of an AEAQECC, which is associated with the dimension of the intersection of the two corresponding linear codes. Two linear codes are said to be a linear l intersection pair if their intersection has dimension l. In this paper, all possible linear l intersection pairs of MDS codes are given. As an application, we give a complete characterization of pure MDS AEAQECCs for all possible parameters.

title: New entanglement assisted quantum MDS codes
abstract: Entanglement assisted quantum error correcting codes (EAQECCs) can be obtained from arbitrary classical linear codes based on the entanglement assisted stabilizer formalism, which greatly promoted

title: An Algorithmic Approach to Entanglement Assisted Quantum Error Correcting Codes from the Hermitian Curve
abstract: We study entanglement assisted quantum error correcting codes (EAQECCs) arising from classical one point algebraic geometry codes from the Hermitian curve with respect to the Hermitian inner product. Their only unknown parameter is c, the number of required maximally entangled quantum states since the Hermitian dual of an AG code is unknown. In this article, we present an efficient algorithmic approach for computing c for this family of EAQECCs. As a result, this algorithm allows us to provide EAQECCs with excellent parameters over any field size.  This work was supported in part by the Spanish Grant PGC2018  UE) by the Spanish MINECO Grant RYC 2016 20208 (AEI/FSE/UE) by the Junta de CyL (Spain) Grant VA166G18, and by the European Union's Horizon 2020 research and innovation programme, under grant agreement QUARTET No 862644.

title: Some New Entanglement Assisted Quantum Error Correcting MDS Codes with Length \frac {q^{2}+1}{13}
abstract: Entanglement assisted quantum maximum distance separable (MDS) codes form a significant class of quantum codes. By using constacyclic codes, we construct some new classes of q ary entanglement assisted quantum error correcting MDS codes. Most of these codes are new in the sense that their parameters are not covered by the codes available in the literature.

title: Four classes of new entanglement assisted quantum optimal codes
abstract: Entanglement assisted quantum error correcting codes (EAQECCs) provide a general framework for quantum code construction, which overcome certain self orthogonal restriction. It becomes one main task in quantum error correction to find EAQECCs with good parameters, especially entanglement assisted quantum maximum distance separable (EAQMDS) codes. In this work, we construct four new families of EAQECC codes with flexible parameters in view of negacyclic codes. It is worth pointing out that those EAQECCs are EAQMDS codes when $d\le (n+2)/2$ d n 2 2 By exploring the selection of defining sets, the constructed EAQECCs possess larger minimum distance in contrast with the known results in the literatures.

title: Asymmetric entanglement assisted quantum codes: bound and constructions
abstract: The theory of quantum error correcting codes has been extended to asymmetric quantum channels qubit flip and phase shift errors may have equal or different probabilities. Previous work in constructing quantum error correcting codes has focused on code constructions for symmetric quantum channels. Recently, Galindo et al. introduced the concept of asymmetric entanglement assisted quantum error correcting (AEAQEC) code, and gave a Gilbert Varshamov bound for AEAQEC codes. Then they present the explicit computation of the parameters of AEAQEC codes coming from BCH codes. In this paper, we first establish a bound for pure AEAQEC codes similar to the quantum Singleton bound, and introduce the definition of pure AEAQEC MDS codes. Then we construct three new families of AQEAEC codes by means of Vandermonde matrices, extended GRS codes and cyclic codes. The AEQAEC codes here have better parameters than the ones available in the literature.

title: Quantum Codes and Entanglement Assisted Quantum Codes Derived from One Generator Quasi Twisted Codes
abstract: In this paper, we consider a special class of one generator quasi twisted (QT) codes of index 2 and explore their algebraic structure. By studying the form of Hermitian dual codes, a sufficient condition for self orthogonality with Hermitian inner product is proposed. Using some one generator QT codes, we construct some quantum codes on small finite fields. Moreover, a new method is provided to construct maximal entanglement entanglement assisted quantum codes via the class of QT codes. By comparison, our quantum codes and maximal entanglement entanglement assisted quantum codes have better parameters than any known codes.

title: Entanglement assisted quantum MDS codes from generalized Reed Solomon codes
abstract: In this paper, some new classes of entanglement assisted quantum MDS codes (EAQ MDS codes for short) are constructed via generalized Reed Solomon codes over finite fields of odd characteristic. Among our constructions, there are many EAQMDS codes with new lengths. Moreover, some of these EAQMDS codes have larger minimum distance than known results.

title: New Entanglement Assisted Quantum MDS Codes with Maximal Entanglement
abstract: The construction of maximum distance separable (MDS) linear complementary dual (LCD) codes and entanglement assisted quantum MDS (EAQMDS) codes have been of a great interest. In this paper, for arbitrary prime power q we construct two new families of MDS Hermitian LCD codes of length n q 2 1 l $n=\frac {q^{2}+1}\lambda and n q 2 1 r $n=\frac {q^{2} 1}{r} where r q 1. By applying the obtained MDS Hermitian LCD codes to the EAQMDS codes, we derive new maximal entanglement EAQMDS codes of parameters q 2 1 l q 2 1 l l 1 l l 1 q \left \kern 0.30em\left \frac {q^{2}+1}\lambda \frac {q^{2}+1}\lambda l+1,l;l 1}\right \kern 0.30em\right ]_{q} where 2 l q 2 1 2 l 2 l $2\leq l\leq \left \lfloor \frac {q^{2}+1+2\lambda {2\lambda \right \rfloor and q 2 1 r q 2 1 r g g 1 g q \left \kern 0.30em\left \frac {q^{2} }1}{r}\frac  }1}{r} \gamma \gamma +1;\gamma \right \kern 0.30em\right ]_{q} where 1 g q 2 1 2 r $1\leq \gamma \leq \frac {q^{2} 1}{2r}

title: Optimal Entanglement Assisted Quantum Codes With Larger Minimum Distance
abstract: Entanglement assisted quantum error correcting code (EAQECC) is a new type quantum code and can be constructed from arbitrary linear codes by sharing entangled states <inline formula> <tex math notation="LaTeX"{c} /tex math>/inline formula> in advance. In this letter, we explore a family of entanglement assisted quantum error correcting codes (EAQECCs) with length <inline formula> <tex math notation="LaTeX"(q^{2} 1)/12$ /tex math>/inline formula> from negacyclic codes. Compared with known results in the literatures, our EAQECCs are new and have larger minimum distance.