Search

Maximum distance separable (MDS) quantum error-correcting codes (QECCs) and MDS entanglement-assisted QECCs (EAQECCs) play significant roles in quantum information theory. In this paper, we construct several new families of MDS QECCs and MDS EAQECCs by utilizing Hermitian self-orthogonal generalized Reed–Solomon codes. These newly obtained MDS QECCs contain some known classes of MDS QECCs as subclasses and some of them have larger minimum distance. In addition, many q-ary MDS QECCs and MDS EAQECCs in our constructions have length exceeding q + 1 and minimum distance surpassing q 2 + 1 . [ABSTRACT FROM AUTHOR]

In this paper, we construct four families of entanglement-assisted quantum error-correcting codes (EAQECCs) with flexible parameters from negacyclic codes. By selecting different defining sets, our codes are new in the sense that their parameters are not covered by the codes available in the literature. Moreover, the EAQECCs we constructed are optimal and have larger minimum distance compared with the known codes with the same length. [ABSTRACT FROM AUTHOR]

The entanglement-assisted stabilizer formalism can transform arbitrary classical linear codes into entanglement-assisted quantum error correcting codes. In this work, we construct some new entanglement-assisted quantum maximum distance separable codes with length n = q 2 + 1 5 from cyclic codes. Compared with all the previously known parameters with the same length, all of them have flexible parameters and larger minimum distance. [ABSTRACT FROM AUTHOR]

Entanglement-assisted quantum maximum distance separable (MDS) codes form a significant class of quantum codes. By using generalized Reed–Solomon (GRS) codes and extended GRS 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. [ABSTRACT FROM AUTHOR]

Entanglement-assisted quantum error-correcting codes are a generalization of standard stabilizer quantum error-correcting codes, which can be possibly constructed from any classical codes by relaxing the duality condition and utilizing pre-shared entanglement between the sender and the receiver. In this paper, we construct seven new families of entanglement-assisted quantum maximum-distance-separable codes from cyclic codes by exploiting less pre-shared entangled states. Most of these codes are new in the sense that their parameters are not covered by the codes available in the literature. [ABSTRACT FROM AUTHOR]

By generalizing the stabilizer quantum error-correcting codes, entanglement-assisted quantum error-correcting (EAQEC) codes were introduced, which could be derived from any classical linear codes via the relaxation of self-orthogonality conditions with the aid of pre-shared entanglement between the sender and the receiver. In this paper, three classes of entanglement-assisted quantum error-correcting maximum-distance-separable (EAQMDS) codes are constructed through generalized Reed–Solomon codes. Under our constructions, the minimum distances of our EAQMDS codes are much larger than those of the known EAQMDS codes of the same lengths that consume the same number of bits. Furthermore, some of the lengths of the EAQMDS codes are not divisors of q 2 - 1 , which are completely new and unlike all those known lengths existed before. [ABSTRACT FROM AUTHOR]

The hull of a linear code is the intersection of itself with its dual code with respect to certain inner product. Both Euclidean and Hermitian hulls are of theorical and practical significance. In this paper, we construct several new classes of maximum distance separable (MDS) codes via (extended) generalized Reed-Solomon (GRS) codes and determine their Euclidean or Hermitian hulls. As a consequence, four new classes of MDS codes with Hermitian hulls of flexible dimensions and six new classes of MDS codes with Euclidean hulls of flexible dimensions are constructed. As applications, for the former, we further construct four new families of entanglement-assisted quantum error-correcting codes (EAQECCs) and four new families of MDS EAQECCs of length n > q + 1 . Meanwhile, many of the distance parameters of our MDS EAQECCs are greater than ⌈ q 2 ⌉ or q; for the latter, we show some examples on Euclidean self-orthogonal and one-dimensional Euclidean hull MDS codes. In addition, two new general methods for constructing extended GRS codes with (k - 1) -dimensional Hermitian hull and Hermitian self-orthogonal extended GRS codes are also provided. [ABSTRACT FROM AUTHOR]

Entanglement-assisted quantum error-correcting codes as a generalization of stabilizer quantum error-correcting (QEC) codes can improve the performance of stabilizer QEC codes and can be constructed from arbitrary classical linear codes by relaxing the dual-containing condition and using pre-shared entanglement states between the sender and the receiver. In this paper, we construct some families of entanglement-assisted quantum maximum distance separable codes with parameters [ [ q 2 - 1 a , q 2 - 1 a - 2 (d - 1) + c , d ; c ] ] q , where q is an odd prime power with the form q = a m ± l , a = l 2 - 1 or a = l 2 - 1 2 , l is an odd integer, and m is a positive integer. Most of these codes are new in the sense that their parameters are not covered by the codes available in the literature. [ABSTRACT FROM AUTHOR]