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Title: On quantum codes via cyclic codes of arbitrary length over 4 + u 4
Authors: Sharma A.
Bandi R.
Bhaintwal, Maheshanand
Published in: Discrete Mathematics, Algorithms and Applications
Abstract: In this paper, we study cyclic codes over R=4+u4,u2 = 0. A necessary and sufficient condition for a cyclic code over R to contain its dual is determined. The odd and even length cases are discussed separately to obtain above condition. It is shown that Gray image of a cyclic code over R containing its dual is a linear code over 4 which also contains its dual. We have then obtained the parameters of corresponding CSS-quantum codes over 4. By augmentation, we construct codes with dual-containing property from codes of smaller size containing their duals. Through this construction, we have obtained some optimal quantum codes over 4. Some examples have been given to illustrate the results. © 2018 World Scientific Publishing Company.
Citation: Discrete Mathematics, Algorithms and Applications (2018), 10(3): -
Issue Date: 2018
Publisher: World Scientific Publishing Co. Pte Ltd
Keywords: Codes over rings
Cyclic codes
Dual containing codes
Quantum codes
ISSN: 17938309
Author Scopus IDs: 55605770443
Author Affiliations: Sharma, A., Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India
Bandi, R., Department of Mathematics, Dr. SPM International Institute of Information Technology, Naya Raipur, India
Bhaintwal, M., Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India
Appears in Collections:Journal Publications [MA]

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