A class of 1-generator right Quasi-polycyclic Codes

In the present paper, we interest in right l-quasipolycyclic (((a) over right arrow, l)-QP) codes of length n = ml induced by the vector (a) over right arrow = (a(0), a(1),..., a(m-1)) is an element of F-q(m), over the finite field 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 l-QP codes. Finally, we give some examples as applications of some of the results using the SageMath software.