In a recent paper spreading codes for CDMA systems were constructed based on Hadamard matrices and semi-bent functions. These codes were applicable to synchronous CDMA systems and to quasi-synchronous CDMA systems when a loosely-synchronized code is used. The codes consist of the union of rows of four Hadamard matrices. The codes can be assigned to a regular tessellation of hexagonal cells in such a way that the correlation between codewords assigned to adjacent cells is zero, while the correlation between codewords assigned to non-adjacent cells is small. The use of codewords from four Hadamard matrices allows greater codeword re-use distances than the use of codewords from a single Hadamard matrix. This has advantages for both satellite and terrestrial systems. These codes only support a single data rate. The current paper shows how orthogonal variable spreading factor codes can be created from them by a careful selection of the semi-bent functions used.

Spreading codes for code-division multiple-access (CDMA) systems are constructed based on Hadamard matrices and almost-bent functions. These codes can be assigned to a tessellation of hexagonal cells in such a way that codewords assigned to the same cell or to adjacent cells have zero cross-correlation. The nonzero cross-correlations in the code only apply to pairs of codewords assigned to nonadjacent cells. The codes have four times as many codewords as codes constructed from a single Hadamard matrix, which leads to significantly increased codeword re-use distances in comparison with the conventional use of a single Hadamard matrix with the same number of codewords per cell.