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