Supporting Information for the Paper: Quaternary Constant-Composition Codes with Weight Four and Distances Five or Six

Proposition 1.1: There exists a [2, 1, 1]-GDC(5) of type 2 with size 2t(t − 1) for each t ∈ {9, 11}, which is also an optimal (2t, 5, [2, 1, 1])4-code. Proof: For each t ∈ {9, 11}, let Xt = Z2t, Gt = {{i, t+ i} : i ∈ Zt} and Ct be the set of cyclic (or quasi-cyclic) shifts of the vectors generated by the following vectors respectively. Then (Xt,Gt, Ct) is a [2, 1, 1]-GDC(5) of type 2 with size 2t(t− 1), where