A class of 1-generator right Quasi-polycyclic Codes

In the present paper, we interest in right $\ell$ -quasi-polycyclic $((\vec{a}, \ell)$ - QP) codes of length $n= ml$ induced by the vector $\vec{a}=(a_{0}, a_{1},\ldots, a_{m-1})\in \mathbb{F}_{q}^{m}$ , over the finite field $\mathbb{F}_{q}$ , which forms a generalization of quasi-cyclic, quasi-negacyclic and quasi-twisted codes. After recalling the necessary background on polycyclic and QP codes, we discuss the structure and the enumeration of the 1-generator $\ell$ -QP codes. Finally, we give some examples as applications of some of the results using the SageMath software.