Construction of bivariate symmetric orthonormal wavelets with short support

In this paper, we give a parameterization of the class of bivariate symmetric orthonormal scaling functions with filter size $6\times 6$ using the standard dilation matrix 2I. In addition, we give two families of refinable functions which are not orthonormal but have associated tight frames. Finally, we show that the class of bivariate symmetric scaling functions with filter size $8\times 8$ can not have two or more vanishing moments.