On constacyclic codes over Z4[u]/〈u2−1〉 and their Gray images

We first define a new Gray map from R=Z4+uZ4 to Z42, where u2=1 and study (1+2u)-constacyclic codes over R. Also of interest are some properties of (1+2u)-constacyclic codes over R. Considering their Z4 images, we prove that the Gray images of (1+2u)-constacyclic codes of length n over R are cyclic codes of length 2n over Z4. In many cases the latter codes have better parameters than those in the online database of Aydin and Asamov. We also give a corrected version of a table of new cyclic R-codes published by Özen et al. [7].