A multicarrier direct-sequence code-division multiple-access (MC-DS/CDMA) communications system is provided. A code tree of two-dimensional orthogonal variable spreading factor (2D-OVSF) codes is then generated for the system. To generate the code tree, a set of existing M1×N1 2D-OVSF matrices, in the form of A(i)(M1×N1) for i={1, 2, . . . , K1} is selected as seed matrices. M1 represents the number of available frequency carriers in the MC-DS/CDMA system, and N1 represents a spreading factor code length. Another set of existing M2×N2 2D-OVSF matrices, in the form of B2(i)(M2×N2) for i={1, 2, . . . , K2} is then selected as mapping matrices. The mapping matrices are used to generate corresponding children matrices. These second layer child matrices are M1M2×N1N2 matrices with cardinality K1K2, which are defined by reiterating the relationship: C ( M 1 ⁢ M 2 × N 1 ⁢ N 2 ) ( ( i - 1 ) ⁢ K 2 + 1 ) = B 2 ⁢ ( M 2 × N 2 ) ( 1 ) ⊕ A ( M 1 × N 1 ) ( i ) C ( M 1 ⁢ M 2 × N 1 ⁢ N 2 ) ( ( i - 1 ) ⁢ K 2 + 2 ) = B 2 ⁢ ( M 2 × N 2 ) ( 2 ) ⊕ A ( M 1 × N 1 ) ( i ) ⁢ ⋯ C ( M 1 ⁢ M 2 × N 1 ⁢ N 2 ) ( ( i - 1 ) ⁢ K 2 + K 2 ) = B 2 ⁢ ( M 2 × N 2 ) ( K 2 ) ⊕ A ( M 1 × N 1 ) ( i ) where ⊕ indicates a Kronecker product, and i=1, 2, 3, 4, . . . , K1.