Application of Constacyclic Codes to Quantum MDS Codes
نویسندگان
چکیده
منابع مشابه
New Quantum MDS codes constructed from Constacyclic codes
Quantum maximum-distance-separable (MDS) codes are an important class of quantum codes. In this paper, using constacyclic codes and Hermitain construction, we construct some new quantum MDS codes of the form q = 2am + t, n = q 2 +1 a . Most of these quantum MDS codes are new in the sense that their parameters are not covered be the codes available in the literature.
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Quantum error-correcting codes play an important role in both quantum communication and quantum computation. It has experienced a great progress since the establishment of the connections between quantum codes and classical codes (see [4]). It was shown that the construction of quantum codes can be reduced to that of classical linear error-correcting codes with certain self-orthogonality proper...
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The entanglement-assisted (EA) formalism allows arbitrary classical linear codes to transform into entanglement-assisted quantum error correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this work, we propose a decomposition of the defining set of constacyclic codes. Using this method, we construct four classes of q-ary entanglement-assisted quant...
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Assuming the validity of the MDS Conjecture, the weight distribution of all MDS codes is known. Using a recently-established characterization of asymmetric quantum error-correcting codes, linear MDS codes can be used to construct asymmetric quantum MDS codes with dz ≥ dx ≥ 2 for all possible values of length n for which linear MDS codes over Fq are known to exist.
متن کاملNew quantum mds constacylıc codes
This paper is devoted to the study of the construction of new quantum MDS codes. Based on constacyclic codes over F q2 , we derive four new families of quantum MDS codes, one of which is an explicit generalization of the construction given in Theorem 7 in [22]. We also extend the result of Theorem 3.3 given in [17].
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2015
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2015.2388576