Abstract In this paper, we study a class of skew-cyclic codes over the ring R= Z₄+u Z₄+u^2 Z₄ R = Z 4 + u Z 4 + u 2 Z 4, where u^3=0 u 3 = 0 with an automorphism θ and a derivation δ θ and we call such codes: δ θ -cyclic codes. Some structural properties of the skew polynomial ring Rx, , R x, θ, δ θ are discussed and these codes are considered as left Rx, , R x, θ, δ θ -submodules. Generator and parity-check matrices of a free δ θ -cyclic code of even length over R are determined. A Gray map on R is used to obtain the Z₄ Z 4 -images. Furthermore, these codes are generalized to double skew-cyclic codes. As an application of δ θ -cyclic codes, we have obtained new quaternary linear codes from the Gray images of δ θ -cyclic codes over R and added them to Aydin’s codetable.
ŞAHİNKAYA et al. (2026) studied this question.