Linear codes over Z4 + uZ4: MacWilliams identities, projections, and formally self-dual codes

Linear codes are considered over the ring Z(4) + uZ(4) a nonchain extension of Z(4). Lee weights, Gray maps for these codes are defined and MacWilliams identities for the complete, symmetrized and Lee weight enumerators are proved. Two projections from Z(4) + uZ(4) to the rings Z(4) and F-2 + uF(2) are considered and self-dual codes over Z(4) + uZ(4) are studied in connection with these projections. A non-linear Gray map from Z(4) + uZ(4) to (F-2 + uF(2))(2) is defined together with real and complex lattices associated to codes over Z(4) + uZ(4). Finally three constructions are given for formally self-dual codes over Z(4) + uZ(4) and their Z(4)-images together with some good examples of formally self-dual Z(4)-codes obtained through these constructions. (c) 2014 Elsevier Inc. All rights reserved.