A Family of Constacyclic Codes over ■2m+u■2mand Its Application to Quantum Codes

Let R be the ring ■2m+u■2m,where u2=0.We introduce a Gray map from R to ■22m 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 2 mn.We also prove that every code of length 2 mn 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.