About on the obtaining of some quantum code parameters from (−2vm−1 + 1)-constacyclic codes over the ring R = 𝔽q + v𝔽q + · · · + vm−1𝔽q

In this study, the hull dimensions of (−2v^m−1 +1)-constacyclic codes over the ring R = 𝔽_q + v𝔽_q + · · · + v^m−1𝔽_q with v^m = v are determined. In addition, by using a special Gray map, a necessary condition is given under which the generator polynomial of a (−2v^m−1 + 1)-constacyclic code over R yields, through the polynomial representation of the Gray map, the generator polynomial of the corresponding cyclic code over F_q. Later, an example is presented showing that the parameters of a quantum error-correcting code over F_q can be obtained from a (−2v^m−1 +1)-constacyclic code over R by means of the X-construction method. Furthermore, the case in which the number of (−2v^m−1 + 1)-constacyclic codes of length n over R equals the number of cyclic codes of length 2n over F_q is examined, and an example is provided in which the parameters of the quantum error-correcting codes arising from those cyclic codes—which are Gray images of (−2v^m−1 + 1)-constacyclic codes over R—are presented.