\(F_3R\)-skew cyclic codes (Q516622)

Summary: In this paper, a new class of skew-cyclic codes, termed as \(F_3R\)-skew cyclic codes, is defined, where \(R\) denotes the ring \(F_3+uF_3,u^2=u\). These codes are of length \(\alpha+\beta\) and are submodules of the \(R\)-module \(F_3^\alpha R^\beta\). We study some structural properties of skew cyclic codes over \(R\) and \(F_3R\)-skew cyclic codes. The generator polynomials of these codes are studied. Some examples are given to illustrate the results. An optimal ternary code is obtained as the Gray image of an \(F_3R\)-skew cyclic code.