A Family of Constacyclic Codes over F_2^m + uF_2^m and Its Application to Quantum Codes

Let R be the ring F_2^m + uF_2^m, where u²=0. We introduce a Gray map from R to F₂²m and study (1 + u)-constacyclic codes over R. It is proved that the image of a (1 + u)-constacyclic code length n over R under the Gray map is a distance-invariant binary quasicyclic code of index m and length 2mn. We also prove that every code of length 2mn which is the Gray image of cyclic codes over R of length n is permutation equivalent to a binary quasi-cyclic code of index m. Furthermore, a family of quantum error-correcting codes obtained from the Calderbank-Shor-Steane (CSS) construction applied to (1 + u)-constacyclic codes over R.