Infinite families of MDR cyclic codes over Z4 via constacyclic codes over Z4[u]/⟨u2-1⟩

We study alpha-constacyclic codes over the Frobenius non-chain ring R := Z(4)[u]/< u(2) - 1 > for any unit alpha of R. We obtain new MDR cyclic codes over Z(4) using a close connection between alpha-constacyclic codes over R and cyclic codes over Z(4). We first explicitly determine generators of all alpha-constacyclic codes over R of odd length n for any unit alpha of R. We then explicitly obtain generators of cyclic codes over Z(4) of length 2n by using a Gray map associated with the unit alpha. This leads to a construction of infinite families of MDR cyclic codes over Z(4), where a MDR code means a maximum distance with respect to rank code in terms of the Hamming weight or the Lee weight. We obtain 202 new cyclic codes over Z(4) of lengths 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50 and 54 by implementing our results in Magma software; some of them are also MDR codes with respect to the Hamming weight or the Lee weight. (C) 2019 Elsevier B.V. All rights reserved.