Two-sided Galois duals of multi-twisted codes

Abstract Galois duals of Multi-twisted (MT) codes are considered in this study. We describe a MT code $$\mathcal {C}$$ C as module over principal ideal domain. Hence, has generator polynomial matrix (GPM) $$\textbf{G}$$ G that satisfies an identical equation. prove GPM formula for the Euclidean dual {C}^\perp $$ ⊥ using equation Hermite normal form . Next, we aim to replace with dual. The inner product is asymmetric form, so distinguish between right and left duals. show well but possibly different shift constants. Some interconnected identities linear established also introduce two-sided use condition makes MT, then its GPM. Two special cases studied, one when trivially intersect other they coincide. A necessary sufficient equality any code.