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

摘要

Let p be an odd prime, q = p(m), R = F-q + uF(q) with u(2) = 1, and S = F-q + uF(q) + vF(q) + uvF(q) with u(2) = 1; v(2) = 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 F-q.