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Entanglement-assisted quantum error-correcting codes (abbreviate to EAQECCs) expand the usual paradigm of quantum error correction by allowing two parties to make use of pre-shared entanglement. It is well-known that we can construct an EAQECC from arbitrary classical linear code. In this paper, we construct several classes of entanglement-assisted quantum MDS (EAQMDS) codes by utilizing generalized Reed-Solomon (GRS) codes. The main contribution of the paper is extend the code length of EAQMDS in the literature (Guo et al. 2019). Consequently, the results show that almost all of these EAQMDS codes are new in the sense that the parameters of these codes are not covered by the previously known ones. [ABSTRACT FROM AUTHOR]

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 R e , q = F q [ u ] / 〈 u e − 1 〉 where m, e ≥ 2 are integers. We decompose the ring into a direct sum of local rings, and consequently, skew constacyclic codes over that ring into a direct sum of skew constacyclic codes over local rings. This decomposition yields the structure of Euclidean duals of skew constacyclic codes and further a necessary and sufficient condition to contain their duals. From an application point of view, we apply the CSS (Calderbank-Shor-Steane) construction on Gray images of dual containing skew constacyclic codes and obtain many quantum codes improving the best-known codes in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study cyclic codes over a finite non-chain ring F p m + v F p m with v2 = 1 and find new and better quantum error-correcting codes than previously known quantum error correcting codes over F p m . Therewith, we characterize the LCD codes and obtain many new LCD codes. Also, we prove that the Gray map of an LCD code of length n over F p m + v F p m is an LCD code of length 2n over F p m . [ABSTRACT FROM AUTHOR]

In this paper we analyse the performance of quantum low-density parity-check (LDPC) codes over quantum memory channels for correcting correlated errors, where the quantum LDPC codes we use are the hypergraph product quantum LDPC codes. We generalize the classical Gilbert-Elliot markovian memory channel to the quantum Gilbert-Elliot channel and use it to model the memory effect in quantum memory channels. The simulation results show the memory effects in quantum GE channels has a bad effect to the performance of hypergraph product quantum LDPC codes. Then we propose a concatenation scheme by serially concatenating two hypergraph product quantum LDPC codes and it is shown that the serial concatenation scheme can improve the performance of hypergraph product quantum LDPC codes and lower down the error floor over quantum GE channels. [ABSTRACT FROM AUTHOR]

If we fix the code length n and dimension k, maximum distance separable (briefly, MDS) codes form an important class of codes because the class of MDS codes has the greatest error-correcting and detecting capabilities. In this paper, we establish all MDS constacyclic codes of length ps over F p m . We also give some examples of MDS constacyclic codes over finite fields. As an application, we construct all quantum MDS codes from repeated-root codes of prime power lengths over finite fields using the CSS and Hermitian constructions. We provide all quantum MDS codes constructed from dual codes of repeated-root codes of prime power lengths over finite fields using the Hermitian construction. They are new in the sense that their parameters are different from all the previous constructions. Moreover, some of them have larger Hamming distances than the well known quantum error-correcting codes in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we construct optimal or almost optimal dual-containing cyclic codes from cyclotomic classes of order r. Based on these cyclic codes constructed, we obtain many new quantum codes comparing with the known literatures. Furthermore, we construct some quantum synchronizable codes with good error-correcting ability towards bit errors and phase errors by a pair of cyclic codes with special containing property. [ABSTRACT FROM AUTHOR]

In this paper, two families of Hermitian dual-containing Bose-Chau- dhuri-Hocquenghem (BCH) codes with length n = a ⋅ q 2 + 1 2 and n = b (q2 + 1) are studied, where odd a∣(q − 1) for odd prime power q and b∣ (q + 1) for even prime power q, respectively. Using these non-narrow-sense BCH codes, some new quantum BCH codes are constructed. Most of these quantum codes have better parameters than the ones in the literature. [ABSTRACT FROM AUTHOR]

Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. The paper is devoted to the construction of new quantum MDS codes based on classical constacyclic codes and cyclic codes over Fq2. We construct a family of new quantum MDS codes with length n=q2+1a, which is a generalization of results in Zhang and Ge (IEEE Trans. Inf. Theory 61(9):5224-5228, 2015), Chen et al. (IEEE. Trans. Inf. Theory 61:1474-1484, 2015). Most of these quantum MDS codes are new in the sense that their parameters are not covered by the quantum codes available in the literature. [ABSTRACT FROM AUTHOR]

Steganography has been proposed as a data hiding technique. As a derivation, quantum steganography based on quantum physics has also been proposed. In this paper, we extend the results in presented (Mihara, Phys. Lett. 379, 952 2015) and propose a multi-party quantum steganography technique that combines quantum error-correcting codes with entanglement. The proposed protocol shares an entangled state among n +1 parties and sends n secret messages, corresponding to the n parties, to the other party. With no knowledge of the other secret messages, the n parties can construct a stego message by cooperating with each other. Finally, we propose a protocol for sending qubits using the same technique. [ABSTRACT FROM AUTHOR]

In this paper, we propose a quantum secure direct communication scheme based on six-qubit decoherence-free (DF) states, which can protect communication against collective decoherence noise. With the combination of DF states and error-correcting code (ECC), it achieves a fault tolerant quantum secure direct communication to prevent collective decoherence noise, limited photon loss and other noise. [ABSTRACT FROM AUTHOR]

In this paper, we propose a scheme for quantum private comparison using phase encoding. The analysis indicates that the scheme is secure, and can prevent some familiar attacks. With the use of error-correcting code (ECC), it achieves a limited fault tolerant quantum private comparison. The scheme is easy to be realized in current experiments. [ABSTRACT FROM AUTHOR]