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Title: On the structure of cyclic codes over 𝔽<inf>q</inf>RS and applications in quantum and LCD codes constructions
Authors: Hai Q. Dinh
Tushar Bag
Ashish Kumar Upadhyay
Ramakrishna Bandi
Warattaya Chinnakum
Keywords: Computer Science
Materials Science
Issue Date: 1-Jan-2020
Abstract: © 2013 IEEE. Let p be an odd prime, q=pm, R=𝔽q}+u𝔽q with u2=1, and S= Fq+u 𝔽q+v𝔽q+uv𝔽q with u2=1, v2=1, uv=vu. In this paper, 𝔽qRS-cyclic codes over 𝔽qRS are studied. As an application, we present a construction of quantum error-correcting codes (QECCs) from the 𝔽qRS-cyclic codes over 𝔽qRS, which provides new QECCs. We also consider linear complementary dual (LCD) codes from the 𝔽qRS-cyclic codes over 𝔽qRS. Among others, we construct a Gray map over 𝔽qRS and discuss the Gray images of 𝔽qRS-cyclic codes over 𝔽q
ISSN: 21693536
Appears in Collections:CMUL: Journal Articles

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