In recent years, there have been intensive activities in the area of constructing quantum maximum distance separable(mds for short) codes from constacyclic mdscodes through the Hermitian construction. In this paper, ...
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In recent years, there have been intensive activities in the area of constructing quantum maximum distance separable(mds for short) codes from constacyclic mdscodes through the Hermitian construction. In this paper, a new class of quantum mds code is constructed, which extends the result of [Theorems 3.14–3.15, Kai, X., Zhu, S., and Li,P., IEEE Trans. on Inf. Theory, 60(4), 2014, 2080–2086], in the sense that our quantum mds code has bigger minimum distance.
quantum mds codes are an important family of quantumcodes. In this paper, using generalized Reed-Solomon codes and Hermitian construction, we construct seven classes of quantum mds codes. All of them provide large mi...
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quantum mds codes are an important family of quantumcodes. In this paper, using generalized Reed-Solomon codes and Hermitian construction, we construct seven classes of quantum mds codes. All of them provide large minimum distance and most of them are new in the sense that the parameters of quantumcodes are different from all the previously known ones.
The construction of quantum mds codes has been studied by many authors. We refer to the table in page 1482 of (IEEE Trans Inf Theory 61(3):1474-1484, 2015) for known constructions. However, there have been constructed...
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The construction of quantum mds codes has been studied by many authors. We refer to the table in page 1482 of (IEEE Trans Inf Theory 61(3):1474-1484, 2015) for known constructions. However, there have been constructed only a few q-ary quantummds [[n, n - 2d + 2, d]](q) codes with minimum distances d > q/2 for sparse lengths n > q + 1. In the case n = q(2)-1/m where m vertical bar q + 1 or m vertical bar q - 1 there are complete results. In the case n = q(2)-1/m while m vertical bar q(2) - 1 is neither a factor of q - 1 nor q + 1, no q-ary quantum mds code with d > q/2 has been constructed. In this paper we propose a direct approach to construct Hermitian self-orthogonal codes over F(q)2. Then we give some newq-ary quantumcodes in this case. Moreover many newq-ary quantum mds codes with lengths of the form w(q(2)-1)/u and minimum distances d > q/2 are presented.
quantum maximum-distance-separable (mds) codes form an important class of quantumcodes. To get q-ary quantum mds codes, one of the effective ways is to find linear mdscodes C over F-q2 satisfying C-perpendicular to ...
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quantum maximum-distance-separable (mds) codes form an important class of quantumcodes. To get q-ary quantum mds codes, one of the effective ways is to find linear mdscodes C over F-q2 satisfying C-perpendicular to H subset of C, where C-perpendicular to H denotes the Hermitian dual code of C. For a linear code C of length n over F q2, we say that C is a dual-containing code if C-perpendicular to H is an element of C and C not equal F-q2(n). Several classes of new quantum mds codes with relatively large minimum distance have been produced through dual-containing constacyclic mdscodes. These works motivate us to make a careful study on the existence conditions for dual-containing constacyclic codes. We obtain necessary and sufficient conditions for the existence of dual-containing constacyclic codes. Four classes of dual-containing constacyclic mdscodes are constructed and their parameters are computed. Consequently, the quantum mds codes are derived from these parameters. The quantum mds codes exhibited here have minimum distance bigger than the ones available in the literature.
The construction of quantum maximum distance separable (mds for short) codes is one of the hot issues in quantum information theory. As far as we know, researchers have done a lot of constructive work in the construct...
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The construction of quantum maximum distance separable (mds for short) codes is one of the hot issues in quantum information theory. As far as we know, researchers have done a lot of constructive work in the construction of quantum mds codes. However, the known results do not cover all parameters. In this paper, we propose an efficient construction implemented by concatenating two existing quantum mds codes. Compared to a previous work (Fang and Luo in quantum Inf Process 19(1):16, 2020), we relax the restrictions of the construction and propose some new quantum mds codes.
One central theme in quantum error correction is to construct quantumcodes that have large minimum distances. It has been a great challenge to construct new quantum maximum-distance-separable (mds) codes. Recently, s...
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One central theme in quantum error correction is to construct quantumcodes that have large minimum distances. It has been a great challenge to construct new quantum maximum-distance-separable (mds) codes. Recently, some quantum mds codes have been constructed from constacyclic codes. Under these constructions, one of the most important problems is to ensure these constacyclic codes are Hermitian dual-containing. This paper presents a method for determining the maximal designed distance of graphic mdscodes from constacyclic codes with fixed n and q. From the method, we can get not only those known quantum mds codes from constacyclic codes but also a new class of quantum mds code from Hermitian dual-containing mds constacyclic code.
quantum maximum-distance-separable (mds) codes play an important role in the quantumcodes. The previous quantum mds codes had been constructed according to q is odd or even. However, such classification omits to cons...
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quantum maximum-distance-separable (mds) codes play an important role in the quantumcodes. The previous quantum mds codes had been constructed according to q is odd or even. However, such classification omits to consider some special categories of quantum mds codes. Because of this, we will discuss the other classifications of q. In this paper, we construct some new q-ary quantum mds codes from generalized Reed-Solomon codes by using Hermitian construction, and prove that these quantum mds codes have minimum distance greater than q/2, where q =-1(mod3).
quantum error-correcting codes and entanglement-assisted quantum error-correcting codes have important applications in quantum computing and quantum communication. In this paper, we construct several classes of quantu...
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quantum error-correcting codes and entanglement-assisted quantum error-correcting codes have important applications in quantum computing and quantum communication. In this paper, we construct several classes of quantum mds codes and entanglement-assisted quantum mds codes by using generalized Reed-Solomon codes. The parameters of most of the codes constructed are new.
The construction of quantum error-correcting codes has been an active field of quantum information theory since the publication of [1, 2, 3]. It is becoming more and more difficult to construct some new quantummds co...
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The construction of quantum error-correcting codes has been an active field of quantum information theory since the publication of [1, 2, 3]. It is becoming more and more difficult to construct some new quantum mds codes with large minimum distance. In this paper, based on the approach developed in the paper [4], we construct several new classes of quantum mds codes. The quantum mds codes exhibited here have not been constructed before and the distance parameters are bigger than q/2.
In this paper, we present three new classes of q-ary quantum mds codes utilizing generalized Reed-Solomon codes satisfying Hermitian self-orthogonal property. Among our constructions, the minimum distance of some q-ar...
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In this paper, we present three new classes of q-ary quantum mds codes utilizing generalized Reed-Solomon codes satisfying Hermitian self-orthogonal property. Among our constructions, the minimum distance of some q-ary quantum mds codes can be bigger than q/2 + 1. Comparing to previous known constructions, the lengths of codes in our constructions are more flexible.
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