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

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