LAUSR

Let R be an arbitrary commutative finite chain ring and $$\gamma $$γ a fixed generator of the maximal ideal of R. Suppose s is the nilpotency index of $$\gamma $$γ and F is the residue field of R modulo its ideal $$\gamma R$$γR, i.e. $$F = R / \gamma R$$F=R/γR, $$\vert F \vert = q$$|F|=q with $$q=p^{\alpha }$$q=pα for some prime number p and let $$R^{\times }$$R× denote the multiplicative group of units of R. For any $$\omega \in R^{\times }$$ω∈R× and $$t \ge \lceil \frac{s}{2}\rceil $$t≥⌈s2⌉, the structural properties and dual codes of $$(1+ \omega \gamma ^{t})$$(1+ωγt)-quasi-twisted (QT) codes of length $$n=\ell m$$n=ℓm, with $$(m, p)=1$$(m,p)=1, over R are given. The key idea is to view a $$(1 + \omega \gamma ^{t})$$(1+ωγt)-QT code over R as a linear code over $$R_{m} = R[x] / \langle x^{m} - (1 + \omega \gamma ^{t}) \rangle $$Rm=R[x]/⟨xm-(1+ωγt)⟩. Furthermore, given the decomposition of a $$(1+ \omega \gamma ^{t})$$(1+ωγt)-QT code, we provide the decomposition of its dual code. As a result, a characterization of self-dual $$(1+ \omega \gamma ^{t})$$(1+ωγt)-QT codes over a finite chain ring R, with $$(1+ \omega \gamma ^{t})=(1+ \omega \gamma ^{t})^{-1}$$(1+ωγt)=(1+ωγt)-1, is provided. By using the Chinese remainder theorem or the discrete Fourier transform, the ring $$R[x] / \langle x^{m} - (1 + \omega \gamma ^{t}) \rangle $$R[x]/⟨xm-(1+ωγt)⟩ can be decomposed into a direct sum of finite chain rings. The inverse transform of the discrete Fourier transform produces a method for deriving $$(1+ \omega \gamma ^{t})$$(1+ωγt)-QT codes from codes of lower lengths.