Abstract

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, 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