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On the Structure of Cyclic Codes Over 𝔽qRS and Applications in Quantum and LCD Codes Constructions

Authors: 

Hai Q. Dinh, Tushar Bag, Ashish Kumar Upadhyay, Ramakrishna Bandi, Warattaya Chinnakum

Source title: 
IEEE Access, 8: 18902-18914, 2020 (ISI)
Academic year of acceptance: 
2020-2021
Abstract: 

Let p be an odd prime, q = pm , R = Fq + uFq with u2 = 1, and S = Fq + uFq + vFq + uvFq with u2 = 1, v2 = 1, uv = vu. In this paper, Fq RS-cyclic codes over Fq RS are studied. As an application, we present a construction of quantum error-correcting codes (QECCs) from the Fq RS-cyclic codes over Fq RS, which provides new QECCs. We also consider linear complementary dual (LCD) codes from the Fq RS-cyclic codes over Fq RS. Among others, we construct a Gray map over FqRS and discuss the Gray images of Fq RS-cyclic codes over Fq .