Constructions of Formally Self-Dual Codes over Z₄ and Their Weight Enumerators

We present three explicit methods for construction of formally self-dual codes over Z₄. We characterize relations between Lee weight enumerators of formally self-dual codes of length n+Z4 and those of length n+2; the first two construction methods are based on these relations. The last construction produces free formally self-dual codes over Z₄. Using these three constructions, we can find free formally self-dual codes over Z₄, as well as non-free formally self-dual codes over Z₄ of all even lengths. We find free or non-free formally self-dual codes over Z₄ of lengths up to ten using our constructions. In fact, we obtain 46 inequivalent formally self-dual codes whose minimum Lee weights are larger than self-dual codes of the same length. Furthermore, we find 19 non-linear extremal binary formally self-dual codes of lengths 12, 16, and 20, up to equivalence, from formally self-dual codes over Z₄ by using the Gray map.