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An application of constacyclic codes to entanglement-assisted quantum MDS codes

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Abstract

The constructions of entanglement-assisted quantum codes have been studied intensively by researchers. Nevertheless, it is hard to determine the number of shared pairs required for constructing entanglement-assisted quantum codes from linear codes. In this paper, by making use of the notion of decomposition for defining sets of constacyclic codes, we construct several new families of entanglement-assisted quantum MDS codes from constacyclic codes, some of which are of minimum distances greater than \(q+1\). Moreover, we tabulate their parameters to illustrate what we find in this paper.

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Authors and Affiliations

  1. Department of Mathematics, Yildiz Technical University, 34220, Esenler, Turkey

    Mustafa Sarı & Emre Kolotoğlu

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  1. Mustafa Sarı
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  2. Emre Kolotoğlu
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Correspondence to Mustafa Sarı.

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Communicated by Thomas Aaron Gulliver.

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Sarı, M., Kolotoğlu, E. An application of constacyclic codes to entanglement-assisted quantum MDS codes. Comp. Appl. Math. 38, 75 (2019). https://doi.org/10.1007/s40314-019-0837-1

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  • DOI: https://doi.org/10.1007/s40314-019-0837-1

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