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Title: New quantum codes from self-orthogonal cyclic codes over Fq2[u]/⟨uk⟩
Authors: Biswas S.
Bhaintwal, Maheshanand
Published in: Quantum Information Processing
Abstract: In this paper, we propose a construction of q-ary quantum codes from Hermitian self-orthogonal cyclic codes over the finite chain ring R=Fq2[u]/⟨uk⟩, with uk= 0 , where Fq2 is a finite field with q2 elements, q= pm, p a prime. A Gray map from R to Fq2k is defined. Some characterizations of cyclic codes over R have been given in terms of their different types of generators. The structure of their dual codes has also been determined, and a necessary and sufficient condition for these codes to be self-orthogonal is presented. The construction of quantum codes is derived by applying Hermitian construction to the Gray images of self-orthogonal cyclic codes over R. From this construction, we have been able to obtain some new quantum codes with better parameters than some presently known comparable best codes available in the literature. Some of these codes have been given as examples, and the others have been given in the form of two tables. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Citation: Quantum Information Processing, 20(9)
Issue Date: 2021
Publisher: Springer
Keywords: cyclic code
Gray map
quantum codes
Self-orthogonal codes
ISSN: 15700755
Author Scopus IDs: 57221230279
Author Affiliations: Biswas, S., Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India
Bhaintwal, M., Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India
Funding Details: The authors would like to thank the referees for their helpful comments and suggestions that greatly improved the presentation of the paper.
Corresponding Author: Biswas, S.; Department of Mathematics, India; email:
Appears in Collections:Journal Publications [MA]

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